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.