**Topics Covered**: Main classes of groups , Permutation groups , Matrix groups ,Transformation groups , Abstract groups ,Topological and algebraic groups , Branches of group theory , Finite group theory , Representation of groups , Lie theory , Combinatorial and geometric group theory , Connection of groups and symmetry , Applications of group theory , Galois theory , Algebraic topology , Algebraic geometry and cryptography , Algebraic number theory Ring theory.