Finite Group Theory is a branch of mathematics that studies groups with a finite number of elements. A group is a set equipped with an operation that combines any two elements to form a third element, satisfying certain conditions like closure, associativity, identity, and invertibility. Finite groups are essential in various areas of mathematics and science, including algebra, geometry, and physics. One of the key results in Finite Group Theory is Cauchy's theorem, which states that if a prime number divides the order of a finite group, then the group contains an element of that prime order. This theory also explores concepts like group homomorphisms, normal subgroups, and simple groups, which help classify and understand the structure of finite groups.