Theory of groups:

The representation theory of groups is a part of mathematics which examines how groups act on given structures; a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element, and that satisfies 4 conditions (the group axioms): closure, associativity, identity and invertibility.  A familiar examples of a group is the set of integers together with the addition operation, but the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, applies much more widely.