This book contains a systematic and comprehensive exposition of Lobachevskian geometry and the theory of discrete groups of motions in Euclidean space and Lobachevsky space. The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry, Riemannian goemetry and group theory. The result is a book which has no rival in the literature. Part I contains the classification of motions in spaces of constant curvature and nontraditional topics like the theory of acuteangled polyhedra and methods for computing volumes of nonEuclidean polyhedra. Part II includes the theory of cristallographic, Fuchsian, and Kleinian groups and an exposition of Thurston's theory of deformations. The greater part of the book is accessible to firstyear students in mathematics. At the same time the book includes very recent results which will be of interest to researchers in this field.

Authors: Alekseevskij D.V., Vinberg E.V., Solodovnikov A.S.  Pages: 76 Year: 1993 
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