From the reviews:
„This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive . . . The text is self-contained and very well illustrated.“
— Aslib Book Guide
"The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments.„
— Mathematical Reviews
“We recommend the excellent introduction of the present book for the history of the various contributions, and also for a sketch of the proof itself. . . . This is an important book which had to be written . . . the book contains a lot of material which will be useful for various other directions of research."
— Zentralblatt Math
“Hyperbolic Manifolds and Discrete Groups is an essential text for anyone working in the topology and geometry of 3-manifolds. It is largely self-contained in that it defines all the needed concepts and machinery and often provides proofs of facts that can be found elsewhere in the literature. This book is most valuable for compiling all the needed concepts in one place. This collection is breath-taking in scope … . Kapovich’s book is an excellent, substantial exposition of the varied aspects of the mathematics present.” (Scott Taylor, The Mathematical Association of America, January, 2011)
Hyperbolic Manifolds and Discrete Groups
von Michael KapovichHyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the „Big Monster,“ i. e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology.
The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.