Includes bibliographical references (p. 265-267) and index.

Preamble to the Second Edition Preamble to the First Edition The Basic Spaces The General Mobius Group Length and Distance in H Planar Models of the Hyperbolic Plane Convexity, Area and Trigonometry Non-planar models Solutions to Exercises References; List of Notation Index

The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Mobius transformations, the general Mobius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincare disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications. This updated second edition also features: an expanded discussion of planar models of the hyperbolic plane arising from complex analysis; the hyperboloid model of the hyperbolic plane; a brief discussion of generalizations to higher dimensions; and many new exercises.