A Brief Account of the Historical Development of Pseudospherical Surfaces From 1827 to 1887
璽€œA Brief Account of the Historical Development of Pseudospherical Surfaces From 1827 to 1887璽€ delves into the intricate world of nineteenth-century geometry, tracing the evolution of our understanding of pseudospherical surfaces. This detailed account explores the key properties of these surfaces, including asymptotic curves, lines of curvature, and geodesic curvature, providing a comprehensive overview of the field's development.The book examines the contributions of leading mathematicians like Enneper and Weingarten, shedding light on the concepts of focal surfaces, orthogonal trajectories, and the behavior of ray systems. It covers essential topics such as radii of curvature, the linear element, and tangent planes, offering insights into the geometry of surfaces with constant negative Gaussian curvature.This historical study provides a valuable resource for mathematicians and historians of science, illuminating the foundational work that shaped modern geometry and offering a glimpse into the mathematical landscape of the late 19th century. Its enduring appeal lies in its meticulous treatment of a fascinating and historically significant area of mathematical research.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Elements of Geometry
"Elements of Geometry," by Benjamin Greenleaf, is a comprehensive textbook designed to elucidate the principles of geometry with a strong emphasis on practical application. Originally published in 1874, this edition offers a rigorous exploration of geometric concepts alongside their use in mensuration璽€"the process of measuring lengths, areas, and volumes. This book aims to bridge the gap between theoretical knowledge and real-world problem-solving. Greenleaf's approach makes this text valuable for students and educators seeking a deeper understanding of geometry's relevance. The book's enduring appeal lies in its clear explanations and its focus on making geometry accessible and applicable to everyday calculations and measurements. A classic resource for anyone interested in mastering the fundamentals of geometry.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Discrete and Computational Geometry, 2nd Edition
The essential introduction to discrete and computational geometry--now fully updated and expanded Discrete and Computational Geometry bridges the theoretical world of discrete geometry with the applications-driven realm of computational geometry, offering a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. Beginning with polygons and ending with polyhedra, it explains how to capture the shape of data given by a set of points, from convex hulls and triangulations to Voronoi diagrams, geometric duality, chains, linkages, and alpha complexes. Connections to real-world applications are made throughout, and algorithms are presented independent of any programming language. Now fully updated and expanded, this richly illustrated textbook is an invaluable learning tool for students in mathematics, computer science, engineering, and physics.Now with new sections on duality and on computational topologyProject suggestions at the end of every chapterCovers traditional topics as well as new and advanced materialFeatures numerous full-color illustrations, exercises, and fully updated unsolved problemsUniquely designed for a one-semester classAccessible to college sophomores with minimal backgroundAlso suitable for more advanced studentsOnline solutions manual (available to instructors)
Fundamentals of Coordinate Geometry
Coordinate geometry is the study of geometric figures by plotting them in the coordinate axes.The content of the book is sequentially presented in the book for easy and comprehensive learning.This book forms a strong basis for students, teachers, researchers, and person engaged in the field of mathematics.
Functional Differential Geometry
An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Mis矇rables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.
Geometric Deformations of Discriminants and Apparent Contours
Comp Formal Euclidean Geom (V1)
This book explores three computational formalisms for solving geometric problems. Part I introduces a trigonometric-based formalism, enabling calculations of distances, angles, and areas using basic trigonometry. Part II focuses on complex numbers, representing points in the plane to manipulate geometric properties like collinearity and concurrency, making it particularly useful for planar problems and rotations. Part III covers vector formalism, applying linear algebra to both plane and solid geometry. Vectors are effective for solving problems related to perpendicularity, collinearity, and the calculation of distances, areas, and volumes.Each formalism has its strengths and limitations, with complex numbers excelling in the plane and vectors being more versatile in three-dimensional space. This book equips readers to choose the best approach for various geometric challenges. This book, designed for math majors, especially future educators, is also valuable for gifted high school students and educators seeking diverse proofs and teaching inspiration.
Four-Dimensional Paper Constructions Mobius, Klein & Boy
Explore four-dimensional paper constructions inspired by the work of great mathematicians like M繹bius, Klein, Boy, Hopf, and others. These creations will help you visualize four-dimensional space and beyond, transporting you to higher-dimensional spaces. This book is designed to solidify your foundations in various areas of mathematics and physics, with a particular focus on topology.If you are familiar with higher-dimensional spaces from loving sci-fi stories, you may find the four-dimensional illustrations in this book especially intuitive. Imagine starting on Earth and traveling straight up into the universe -- where would you end up? Perhaps you would travel in one direction only to eventually return to your starting point. Can you imagine what happens during the course of this trip? By engaging with these four-dimensional paper constructions, you will gain a deeper understanding of this fascinating journey.
Geometry and Analysis on Finsler Spaces
Finsler geometry is a Riemannian geometry without quadratic restriction. It was originated from Riemann's ground-breaking 'Habilitation' address in the year 1854 and has many applications in many fields of the natural sciences including physics, psychology and ecology etc. The book is intended to provide basic materials on Finsler geometry for readers who are interested in Riemann-Finsler geometry, and to bring them into the frontiers of the active research on related topics.The book is comprised of three parts. The first part consists of Chapters 1-4, which cover the basic theory of Finsler geometry and important geometric invariants, including Riemannian quantities and non-Riemannian quantities. Chapters 5-6 present the theory of geodesics and comparison theorems, which are fundamental tools to investigate global Finsler geometry. The last part consisting of Chapters 7-9 presents the recent developments in the global analysis, including harmonic functions, the eigenvalue problem and heat flow etc., on Finsler manifolds although the problems discussed are classical.
Geometric Gems (V3)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.
Geometric Gems (V3)
Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.
Lectures on the H-Cobordism Theorem
Important lectures on differential topology by acclaimed mathematician John Milnor These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.
Convexity and Its Applications in Discrete and Continuous Optimization
Using a pedagogical, unified approach, this book presents both the analytic and combinatorial aspects of convexity and its applications in optimization. On the structural side, this is done via an exposition of classical convex analysis and geometry, along with polyhedral theory and geometry of numbers. On the algorithmic/optimization side, this is done by the first ever exposition of the theory of general mixed-integer convex optimization in a textbook setting. Classical continuous convex optimization and pure integer convex optimization are presented as special cases, without compromising on the depth of either of these areas. For this purpose, several new developments from the past decade are presented for the first time outside technical research articles: discrete Helly numbers, new insights into sublinear functions, and best known bounds on the information and algorithmic complexity of mixed-integer convex optimization. Pedagogical explanations and more than 300 exercises make this book ideal for students and researchers.
Lectures on K瓣hler Groups
An introduction to the state of the art in the study of K瓣hler groups This book gives an authoritative and up-to-date introduction to the study of fundamental groups of compact K瓣hler manifolds, known as K瓣hler groups. Approaching the subject from the perspective of a geometric group theorist, Pierre Py equips readers with the necessary background in both geometric group theory and K瓣hler geometry, covering topics such as the actions of K瓣hler groups on spaces of nonpositive curvature, the large-scale geometry of infinite covering spaces of compact K瓣hler manifolds, and the topology of level sets of pluriharmonic functions. Presenting the most important results from the past three decades, the book provides graduate students and researchers with detailed original proofs of several central theorems, including Gromov and Schoen's description of K瓣hler group actions on trees; the study of solvable quotients of K瓣hler groups following the works of Arapura, Beauville, Campana, Delzant, and Nori; and Napier and Ramachandran's work characterizing covering spaces of compact K瓣hler manifolds having many ends. It also describes without proof many of the recent breakthroughs in the field. Lectures on K瓣hler Groups also gives, in eight appendixes, detailed introductions to such topics as the study of ends of groups and spaces, groups acting on trees and Hilbert spaces, potential theory, and L2 cohomology on Riemannian manifolds.
The Universe of Conics
This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries.With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics.This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry.Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.
A Basic Course in Topology
This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geometric objects. It is designed as a bridge between elementary courses in analysis and linear algebra and more advanced classes in algebraic and geometric topology, making it particularly suitable for both undergraduate and graduate mathematics students. The authors employ the modern language of category theory to unify and clarify the concepts presented, with definitions supported by numerous examples and illustrations. The book includes over 170 exercises that reinforce and deepen the understanding of the material.
A Journey Through the Wonders of Plane Geometry
Geometry is often seen as one of the most beautiful aspects of mathematics. This beauty is probably a result of the fact that one can 'see' this aspect of mathematics. Most people are exposed to the very basic elements of geometry throughout their schooling, concentrated in the secondary school curriculum. High schools in the United States offer one year of concentrated geometry teaching, allowing students to observe how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. However, as the course is only one year long, a great amount of geometry remains to be exposed to the general audience. That is the challenge of this book, wherein we will present a plethora of amazing geometric relationships.We begin with the special relationship of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationship between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry.
Modern Approaches to Differential Geometry Related Fields
This volume consists of several papers written by the main participants of the 7th International Colloquium on Differential Geometry and its Related Fields (ICDG2023). Readers will find some papers that cover geometric structures on manifolds, such as quaternionic structures, Kaehler structures, Einstein structures, contact structures and so on, as well as other papers that deal with probability theory and discrete mathematics.In this volume, the authors present their recent research in differential geometry and related fields, offering a comprehensive overview for researchers not only within differential geometry but also across various areas of mathematics and theoretical physics. They aim for this volume to serve as a valuable guide for young scientists beginning their studies and research careers in the related fields. Together with previous proceedings, readers will gain insight into the progress of research on geometric structures in Riemannian manifolds.
Lectures on the H-Cobordism Theorem
Important lectures on differential topology by acclaimed mathematician John Milnor These are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University. These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale. Milnor's goal was to provide a fully rigorous proof in terms of Morse functions. This book remains an important resource in the application of Morse theory.
Recent Topics on Topology - From Classical to Modern Applications
Topology plays a fundamental role in many branches of mathematics and science. In recent years, there has been a resurgence of interest in physics, particularly in condensed matter physics. This book provides an accessible yet rigorous overview of current research in topology, making it an invaluable resource for mathematicians, physicists, and researchers in related fields.
Foundations and Application of Graph Theory
Graph theory, an intriguing and vital area of mathematics, finds its roots in the 18th century, with Leonhard Euler's pioneering work on the Seven Bridges of K繹nigsberg problem. Since then, the field has burgeoned into a versatile and indispensable tool, influencing diverse areas like computer science, biology, sociology, and network theory. The foundational structures and profound applications of graph theory underscore its role as a linchpin in solving modern-day problems.This book, "Foundations and Applications of Graph Theory: From Basics to Advanced Concepts," is born out of a passion for unraveling the elegance and utility of graphs. It aims to bridge the gap between theoretical foundations and practical applications, catering to students, researchers, and professionals alike. With its structured progression from introductory topics to advanced themes, the book serves as both an educational guide and a reference for exploring the depths of graph theory.Through its chapters, readers will journey from the rudiments of graph definitions and properties to specialized topics like magic labeling, graph coloring, and isomorphism. The exploration is not merely theoretical; real-world applications across disciplines are woven throughout to demonstrate the relevance and adaptability of graph theory.-Dr. Rajpal Kosaliya (Author)
K-Theory and Representation Theory
Symmetry is one of the most important concepts in mathematics and physics. Emerging from the 2021 LMS-Bath Summer School, this book provides Ph.D. students and young researchers with some of the essential tools for the advanced study of symmetry. Illustrated with numerous examples, it explores some of the most exciting interactions between Dirac operators, K-theory and representation theory of real reductive groups. The final chapter provides a self-contained account of the representation theory of p-adic groups, from the very basics to an advanced perspective, with many arithmetic aspects.
Solving Problems in Point Geometry
For over two millennia, the complexities of elementary geometry have challenged learners, burdened by the intricacies of auxiliary graphics and cumbersome calculations. Inspired by Leibniz's query, this book introduces a groundbreaking method: point geometry. By operating directly on points, it integrates the strengths of coordinate, vector, and mass point methods, simplifying operations and problem-solving.Central to this method is the identity approach, which streamlines complex problems into concise equations, unlocking multiple propositions with ease. Through meticulously crafted examples, readers are invited to explore the joy of mathematical thinking.Beyond mathematics, point geometry holds promise for artificial intelligence, offering a simple yet rich knowledge representation and reasoning method. With most solutions generated by computer programs, the potential for simplifying reasoning methods is immense, paving the way for a brighter future in both education and AI advancement.In this ambitious endeavor, the authors seek to simplify knowledge representation and reasoning, reduce the burden of learning, and accelerate the progress of artificial intelligence. This book is not just a guide to geometry; it's a catalyst for transformative thinking and discovery.
Solving Problems in Point Geometry
For over two millennia, the complexities of elementary geometry have challenged learners, burdened by the intricacies of auxiliary graphics and cumbersome calculations. Inspired by Leibniz's query, this book introduces a groundbreaking method: point geometry. By operating directly on points, it integrates the strengths of coordinate, vector, and mass point methods, simplifying operations and problem-solving.Central to this method is the identity approach, which streamlines complex problems into concise equations, unlocking multiple propositions with ease. Through meticulously crafted examples, readers are invited to explore the joy of mathematical thinking.Beyond mathematics, point geometry holds promise for artificial intelligence, offering a simple yet rich knowledge representation and reasoning method. With most solutions generated by computer programs, the potential for simplifying reasoning methods is immense, paving the way for a brighter future in both education and AI advancement.In this ambitious endeavor, the authors seek to simplify knowledge representation and reasoning, reduce the burden of learning, and accelerate the progress of artificial intelligence. This book is not just a guide to geometry; it's a catalyst for transformative thinking and discovery.
Projective Geometry
The elements of geometry are points, lines and planes, together with Space and Nothing. In Euclidian geometry, we observe these as if we are point-centred beings concerned with extensive measurement.In non-Euclidian, or projective geometry, we are 'planar' beings observing spatial relations, free of measurement, as dynamic and transformational. This polar opposite vision of intensive space reveals remarkable secrets. In this fascinating and useful book, expert Lawrence Edwards invites the reader to discover these secrets through practical exercises in creative geometry. Topics include: the elements of geometry, duality, collineation, cross ratio, the circling and step measure, conics and the nature of a curve.
Geometrodynamics of Gauge Fields
No detailed description available for "Geometrodynamics of Gauge Fields".
Topological Vector Spaces
With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on vector-valued Hahn-Banach theorems. It also considers different approaches to the Banach-Stone theorem as well as variations of the theorem.The book covers locally convex spaces; barreled, bornological, and webbed spaces; and reflexivity. It traces the development of various theorems from their earliest beginnings to present day, providing historical notes to place the results in context. The authors also chronicle the lives of key mathematicians, including Stefan Banach and Eduard Helly. Suitable for both beginners and experienced researchers, this book contains an abundance of examples, exercises of varying levels of difficulty with many hints, and an extensive bibliography and index.
Math Refresher Workbook for Adults Returning to School
Returning to school as an adult also creates a special learning environment. Adult learners bring their life experiences to the classroom, enriching discussions and broadening perspectives for everyone. Professors value the insights that adult students bring from their diverse backgrounds. This makes the educational experience better for all students.Modern education systems are flexible and support adult learners in ways that were not possible before. With online courses, evening classes, and part-time programs, it's easier for adults to balance school with other responsibilities. This flexibility allows them to continue their education without sacrificing their jobs or family time. Returning to school can also positively affect one's family. Children often see their parents as role models, and a parent going back to school can inspire a lifelong love of learning and perseverance. It shows that it's never too late to pursue your dreams and that education is a lifelong journey.Of course, going back to school as an adult has its challenges. Balancing work, family, and studies requires good time management and dedication. Money can also be an issue, but many companies offer scholarships and financial aid for adult learners. The long-term benefits often outweigh the initial costs, both in career advancement and personal growth.
Differential Forms
Get ready to twist your mind as you dive into The Beauty of Differential Forms. This mind-bending book takes you on a journey through the power and versatility of differential forms, from vectors and vector fields to integration, applications in fluid dynamics, electromagnetism, and general relativity. With a mix of humor and in-depth explanations, this book will have you hooked from start to finish. So, grab a seat, buckle up, and get ready to explore the twisted world of differential forms.
Tilings in Hyperbolic Space in an Arbitrary Dimension
Of a special interest are tilings in hyperbolic n-space. The present work studies tilings in hyperbolic n-space of arbitrary dimension by polytopes. The best behaved tilings are the face-to-face tilings by convex polytopes. The main results of this publication are obtained for tilings (isohedral, non-isohedral, face-to-face, non- face-to- face) in the hyperbolic n-space of arbitrary dimension for any n, (n >= 2) by compact and non-compact polytopes and we describe their discrete isometry groups and properties. Torsion free groups are especially important.
Euclid Transmogrified
This book tells the extraordinary story of how in the mid twentieth century, in a well-developed European country, a mathematically solid system of geometry was altered to such an extent that more than one million students were taught foundationally flawed geometry over more than a quarter of a century. The almost unbelievable situation came about in Ireland in the wake of early postcolonial developments that gave rise to an impressionable and unqualified civil service in a position of power over a nation's educational development. This is a multifaceted tale of a perfect storm within mathematics development in Ireland whose result was so destructive that its ramifications continue to be felt into the twenty-first century, forty years after a report of a Royal Irish Academy commission of professors of mathematics described the matter as a national scandal. Euclid Transmogrified: A National Scandal may be of interest to mathematics teachers, lecturers in mathematics, mathematical historians, lecturers in education, students of mathematical education, administrators of mathematical education, science administrators, science journalists and those educated in mathematics in Ireland, especially those born between 1954 and 2000. https: //sites.google.com/view/euclidtransmogrified1
Lectures on Differential Geometry
This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.
Lectures on Differential Geometry
This book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.
Tutor Book’s
Need help with Geometry? Tutor Book's Geometry is extremely thorough. This book skillfully cover the many concepts that students need to master. Examples, including examples using numbers, are included for those theorems and definitions that skilled tutors and teachers know students find more difficult to understand. Many teaching tips and hints are included to support student learning. Memory tips are given where useful.
Circles, Spheres and Spherical Geometry
This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic themes are used as introductory and motivating topics. The book begins very simply for the reader in the first chapter discussing the notions of inversion and stereographic projection. Here, various classical topics and theorems such as Steiner cycles, inversion, Soddy's hexlet, stereographic projection and Poncelet's porism are discussed. The book then delves into Bend formulas and the relation of radii of circles, focusing on Steiner circles, mutually tangent four circles in the plane and other related notions. Next, some fundamental concepts of graph theory are explained. The book then proceeds to explore orthogonal-cycle representation of quadrangulations, giving detailed discussions of the Brightwell-Scheinerman theorem (an extension of the Koebe-Andreev-Thurston theorem), Newton's 13-balls-problem, Casey's theorem (an extension of Ptolemy's theorem) and its generalizations. The remainder of the book is devoted to spherical geometry including a chapter focusing on geometric probability on the sphere. The book also contains new results of the authors and insightful notes on the existing literature, bringing the reader closer to the research front. Each chapter concludes with related exercises of varying levels of difficulty. Solutions to selected exercises are provided. This book is suitable to be used as textbook for a geometry course or alternatively as basis for a seminar for both advanced undergraduate and graduate students alike.
