The purpose of this course is to introduce the concept of amenability in various algebraic structures and to establish the relation between them with the help of related theorems.

Properties and examples of amenable locally compact groups, amenable semigroups, definition of Banach algebra and examples, concept of module of Banach algebras, concept of derivation of Banach modules, Hochschild cohomology, definition of amenable Banach algebras, Johnson’s theorem, virtual diagonal and approximate diagonal, examples of amenable Banach algebras, hereditary properties of amenable Banach algebras, various notions of amenability in Banach algebras.