Enhanced descriptions from Syndetics:

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty.


This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace.



Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture.


In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology . The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Table of contents provided by Syndetics

• Preface
• Reader's Advisory
• 1 What Is a Manifold? (p. 3)
• 2 Hyperbolic Geometry and Its Friends (p. 43)
• 3 Geometric Manifolds (p. 109)
• 4 The Structure of Discrete Groups (p. 209)
• Glossary (p. 289)
• Bibliography (p. 295)
• Index (p. 301)

Reviews provided by Syndetics

CHOICE Review

Three-dimensional topology studies the global structure of spaces whose local structure coincides with that of the space in which we live. This extraordinarily difficult and active subject has seen many revolutions. Thurston himself authored one of the most important of these revolutions in the late 1970s, work for which he eventually received the Fields Medal, mathematics' most prestigious prize. Oddly, he disseminated his ideas primarily by means of preprints and informal lecture notes and never brought the work to full publication. Indeed, the originality of Thurston's ideas initially baffled other experts, leading to years of reflection on how best to communicate these new methods and arguments. The present volume represents the culmination of nearly two decades of honing his famous but difficult 1978 lecture notes. This beautifully produced, exquisitely organized volume now reads as easily as one could possibly hope given the profundity of the material. An instant classic every library must own! All levels. D. V. Feldman; University of New Hampshire

Author notes provided by Syndetics

William P. Thurston is the Director of the Mathematical Sciences Research Institute in Berkeley, and Professor of Mathematics at the University of California at Davis. He received the Fields Medal in 1982 for his work on hyperbolic structures on 3-manifolds and foliations. Silvio Levy is editor of Experimental Mathematics and of the MSRI book series.