This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva- ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n:::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the...