A finite group is a set equipped with a binary operation that satisfies four key properties: closure, associativity, identity, and invertibility. The set contains a limited number of elements, making it "finite." Each element can be combined with others in the group to produce another element within the same set. Finite groups are fundamental in the field of abstract algebra and have applications in various areas, including cryptography and physics. Examples of finite groups include the symmetric group, which consists of all permutations of a finite set, and cyclic groups, generated by a single element.