On noncommutative geometry

Noncommutative (differential) geometry was introduced by Alain Connes about forty years ago. It is based on the correspondence between topological and geometrical objects (manifolds, bundles, differential forms etc.) and algebraic ones (algebras, modules, Hochschild homology etc.)In the talk we review the basic constructions of noncommutative geometry: C*-algebras, cyclic homology and Chern character.