Group theory, also known as the theory of groups, is a mathematical concept that deals with the study of sets that are equipped with a binary operation that follows certain rules. In the realm of mathematics, several other phrases are often used as synonyms for the term "group theory." These include the theory of symmetry, algebraic structure, abstract algebra, and the theory of automata. Furthermore, group theory forms the basis for the study of various mathematical disciplines such as geometry, number theory, topology, and theoretical physics. Despite having a definition that can often appear abstract and complex, group theory provides a powerful tool for solving problems within these areas of study.