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.