The paper deals with the investigations in the theory of topological groups from 1965 to 1980. The fundamental sections are: group topologies, morphisms, commutativity and its generalizations, finiteness and discreteness conditions for subgroups of locally compact groups, manifolds. One gives the formulation of all the basic results and one indicates the unsolved problems.
Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 20, pp. 3–70, 1982.