Almost every major mathematical theory, from 19th century classical analysis and geometry to the newest abstract constructions of category theory, have recently acquired a ""physical flavour"". In the case of representation theory, two new areas of mathematical physics - the theory of completely integrable systems and string theory - have had a great influence. In addition, the idea of supersymmetry has become a general mathematical principle that has had important ramifications in representation theory. Together with this wave of new connections and new trends in representation theory, more traditional activity, dealing mostly with the study of classical objects, has also flourished. The papers in this volume were written by members of the seminar on representation theory at Moscow University, which has been running continuously since 1961. The papers reflect some of the new influences seen in representation theory today. Among the topics included are representation theory of ""large"" groups, indecomposable representations of the affine unimodular group of the plane, dual objects for certain real reductive Lie groups, and geometrical interpretations of a certain infinite-dimensional Lie algebra.