A finite group is a mathematical structure consisting of a set of elements combined with an operation that satisfies four key properties: closure, associativity, identity, and invertibility. The set has a limited number of elements, meaning it contains a finite number of members. Examples of finite groups include the set of integers modulo n under addition and the symmetric group of permutations on a finite set. In group theory, finite groups are essential for understanding more complex algebraic structures. They can be classified into various types, such as abelian groups, where the operation is commutative, and non-abelian groups, where it is not. The study of finite groups has applications in fields like cryptography and physics.