In this paper, we describe the automorphisms of various classes of finite groups. We introduce the concept of semi direct product on certain groups and use this concept to define the automorphism of certain finite groups. For a semi-direct product of two groups, a short exact sequence splits. A cyclic group of order is written in the direct product of cyclic groups. We compute the automorphism groups of some abelian group and also find the number of automorphisms of some abelian groups.