This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. The reader is assumed to have a basic knowledge of algebra and topology at the first year graduate level of an American university. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The second edition contains hundreds of changes, corrections and new additions include. The exercises have been thoroughly reworked and over 100 new exercises have been added. The author has also prepared a solutions manual which is available to professors who choose to adopt this text for their course. This carefully written textbook has been heavily class-tested and each chapter contains exercises and a section of historical remarks.

Euclidean Geometry.- Spherical Geometry.- Hyperbolic Geometry.- Inversive Geometry.- Isometries of Hyperbolic Space.- Geometry of Discrete Groups.- Classical Discrete Groups.- Geometric Manifolds.- Geometric Surfaces.- Hyperbolic 3-Manifolds.- Hyperbolic n-Manifolds.- Geometrically Finite n-Manifolds.- Geometric Orbifolds.