Foundations of Hyperbolic Manifolds (3^rd Ed., 3rd ed. 2019) Graduate Texts in Mathematics Series, Vol. 149

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.

John G. Ratcliffe is Professor of Mathematics at Vanderbilt University. His research interests range from low-dimensional topology and hyperbolic manifolds to cosmology.

Expands on the second edition by including over 40 new lemmas, theorems, and corollaries, as well as a new section dedicated to arithmetic hyperbolic groups

Offers a highly readable and self-contained exposition of the theoretical foundations of hyperbolic manifolds

Provides readers with over 70 new exercises and features figures in color throughout

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