Definition of a group with examples and  simple properties. Order  of elements in a Group and related theorem.

Subgroups , Cyclic groups, Permutation groups  , Alternating groups.

Cosets, Lagrange’s theorem Normal subgroups , Quotient group.

Homomorphism and Isomorphism, the Fundamental theorem of  homomorphism. Rings:-Definition, Examples and Elementary properties. 

 Integral domain, Fields, Subfields and their simple properties, Subrings. Ideal of a ring, Characteristic of a ring.