Group theory (abstract algebra) is a branch of abstract algebra dedicated to the study of algebraic structures known as groups. A group is formally defined as a set equipped with a binary operation that satisfies four fundamental properties: closure, associativity, the existence of an identity element, and the existence of inverse elements for every element in the set. This field investigates the properties of groups, their subgroups, quotient groups, homomorphisms (structure-preserving maps between groups), and various related concepts such as group actions and group representations. Its significance lies in providing a framework for understanding symmetry, structure, and transformations across diverse areas of mathematics and science, including geometry, topology, number theory, physics, and chemistry.