The first part of this book on Discrete Subgroups of Lie Groups is written by E.B. Vinberg, V.V. Gorbatsevich, and O.V. Shvartsman. Various types of discrete subgroups of Lie groups arise in the theory of functions of complex variables, arithmetic, geometry, and crystallography. Since the foundation of their general theory in the 50-60s of this century, considerable and in many respects exhaustive results were obtained. This development is reflected in this survey. Both semisimple and general Lie groups are considered. Part II on Cohomologies of Lie Groups and Algebras is written by B.L. Feigin and D. B.Fuchs. It contains different definitions of cohomologies of Lie groups and (both finite-dimensional and some infinite-dimensional) Lie algebras, the main methods of their calculation, and the results of these calculations. The book can be useful as a reference and research guide to graduate students and researchers in different areas of mathematics and theoretical physics.

The authors have aimed at systematizing all the basic results on the theory of discrete subgroups of Lie groups and are presenting these in a form convenient for users, making the theory accessible to a wide audience Hence the book will be a standard reference for many years to come

Inhalt
Discrete Subgroups of Lie Groups. E.B. Vinberg, V.V. Gorbatsevich, and O.V. Shvartsman.- Cohomologies of Lie Groups and Lie Algebras. B.L. Feigin and D.B. Fuchs.- References.- Subject Index.- Author Index.