This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work - for the most part in representation theory, group rings, and coding theory - is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.

Table of Contents:
The S. D. Berman work on coding theory and on theory of threshold functions by B. N. Gartshtein and I. I. Grushko Berman's contributions to group representations over fields by G. Karpilovsky S. D. Berman's contribution to the theory of integral representations of finite groups by A. I. Lichtman The work of S. D. Berman on infinite abelian group rings by W. May Berman's work on units in group rings by R. Sandling On $p$-subgroups of finite symmetric and alternating groups by J. G. Berkovic Locally cyclic modules over a valuation ring by S. D. Berman and N. I. Vishnyakova On the modules over a real crossed group algebra by K. Buzasi The minimal number of generators of wreath products of nilpotent groups by K. Buzasi and L. G. Kovacs Torsion free space groups and permutation lattices for finite groups by G. Cliff and A. Weiss Clifford theory and induction from subgroups by E. C. Dade The isomorphism problem for modular group algebras of groups with large centres by V. Drensky Zero divisors in group rings: something old, something new by D. R. Farkas and P. A. Linell The augmentation quotients of finite abelian $p$-groups by A. W. Hales and I. B. S. Passi Free groups in normal subgroups of unit groups and arithmetic groups by B. Hartley On the Bass-Milnor index of abelian $p$-groups by K. Hoechsmann A remark on algebraic geometric codes by G. L. Katsman and M. A. Tsafsman On decomposition of a binomial in a skew polynomial ring by E. S. Kerer The associated graded algebra of a group algebra by L. Krop On nilpotent and soluble subgroups of linear groups over fields of fractions of enveloping algebras and of group rings, I by A. I. Lichtman The structure of $G_0$ for certain polycyclic group algebras and related algebras by M. Lorenz and D. S. Passman The direct factor problem for modular abelian group algebras by W. May On the isomorphism of the semi-simple group algebras of the primary abelian groups by T. Z. Mollov On the canonical irreducible representations of countable locally finite groups and infinite Frobenius group by S. I. Ostrovskaya Generators of subgroups of $U(\Bbb ZG)$ by J. Ritter and S. K. Sehgal Connectivity of the finite group and generalized characters by E. M. Zmud.