Introduction

Group theory is the mathematics of symmetry, which helps both to understand and to simplify physics problems.

Symmetry operations compose associatively; there is an identity operation; and every operation has an inverse that restores the original system. These properties, together with closure, define a `group'. Group theory thus extracts information from the symmetry of a system without solving the full problem (e.g. the Schrödinger equation).

Symmetries are either discrete or continuous, each operation being a group element. Discrete symmetries give discrete groups, which may be finite; continuous symmetries give continuous (Lie) groups.