Group theory is a branch of mathematics that deals with the study of symmetry. It is the study of groups, which are sets of objects with a specific type of symmetry. The objects in a group are called elements, and the symmetry is described by a binary operation called the group operation. A group must have the following three properties: closure, associativity, and the existence of an identity element and inverse elements.
Groups can be used to describe symmetries in many different areas of mathematics and physics, such as in geometry, number theory, and quantum mechanics. For example, the symmetries of a square can be described using a group, as can the symmetries of a crystal. Group theory is also used in the study of abstract algebraic structures, such as rings and fields. Overall Group theory is a powerful tool in understanding the underlying symmetry in the mathematical structures and physical phenomena.