Content: Homological algebra goes back to constructions of algebraic topology to describe topological properties of geometric objects. In the middle of the last century it was recognized that the underlying mechanism can be used with great success in the treatment of problems in various algebraic systems. The publication of Cartan-Eilenberg's monograph "Homological Algebra" in 1955 marked the culmination of this development, since then homological algebra has become an independent theory with its own dynamics and diverse applications.
Expected program: modules; categories and functions; complexes and derived functions; cohomology of groups.