Group theory is a branch of mathematics applicable to sets with symmetric properties. A group is a set with elements (together with an operation) that must obey four rules: closure; associativity (see associative); every element must have an inverse; and there must be an identity element.

The theory was developed by the French mathematician Évariste Galois. Group theory is particularly useful in quantum mechanics, spectroscopy, and theories of elementary particles, but is also used in mathematics to describe many other natural phenomena that have symmetry.