  Group theory was first developed to describe symmetry. A symmetry is a transformation of some structure or object which leaves it unchanged in some respect. A group of symmetry transformations is a mathematical object which consists of the set of transformations, including the identity transformation and the inverse of each transformation, and the operation of composing them, where the result of two composed transformations is itself in the original set. Mathematical objects can be characterised in terms of which symmetry transformations leave them unchanged or invariant.