The present book is devoted to one of the newest branches of variety theory: varieties of group representations. In addition to its intrinsic value, it has numerous connections with varieties of groups, rings and Lie algebras, polynomial identities, group rings, etc., and provides results, methods and ideas that are of interest to a broad algebraic audience. The book presents a clear and detailed exposition of several central topics in the field, leading from initial definitions and problems to the most current advances and developments. Among the topics treated are stable and unipotent varieties, locally finite-dimensional varieties, the finite basis problem, connections with varieties of groups and associative algebras and their applications.