Translations of Mathematical Monographs 2001; 257 pp; hardcover Volume: 200 ISBN10: 0821820389 ISBN13: 9780821820384 List Price: US$104 Member Price: US$83.20 Order Code: MMONO/200
 This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinitedimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for nonEuclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduatelevel courses in geometry. Readership Advanced undergraduates, graduate students, mathematics teachers and researchers interested in geometry. Table of Contents  Introduction
 The Euclidean world
 The affine world
 The projective world
 Conics and quadrics
 The world of nonEuclidean geometries
 The infinitedimensional world
 Addendum
 Solutions, hints, and answers
 Bibliography
 Author index
 Subject index
