內容簡介
This book contains a systematic and comprehensive expositioof Lobachevskiageometry and the theory ofdiscrete groups ofmotions iEuclideaspace and Lobachevsky space. It is divided into two closely related parts: the first treats the geometry ofspaces ofconstant curvature and the second discrete groups of motions of these. The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry, Riemanniageometry and group theory. The result is a book which has no rivalithe literature.Part I contains the classificatioofmotions ispaces ofconstant curvature and non-traditional topics like the theory ofacute-angled polyhedra and methods for computing volumes of non-Euclideapolyhedra. Part II includes the theory of cristallographic, Fuchsian,and Kleiniagroups and aexpositioof Thurston's theory of deformations.The greater part of the book is accessible to first-year students imathematics. At the same time the book includes very recent results which will be ofinterest to researchers ithis field.