This seriously class-tested publication is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A uncomplicated wisdom of algebra and topology on the first 12 months graduate point of an American collage is thought. the 1st half is anxious with hyperbolic geometry and discrete teams. the second one half is dedicated to the speculation of hyperbolic manifolds. The 3rd half integrates the 1st components in a improvement of the speculation of hyperbolic orbifolds. each one bankruptcy includes workouts and a bit of historic comments. A suggestions guide is offered separately.

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