Definition of a Group – Some examples of Groups – Some preliminary lemmas– Basic properties

Subgroups – Cyclic subgroup - Index of a group – Order of an element – Fermat theorem – A Counting Principle - Normal Subgroups and Quotient Groups.

Homomorphism – Cauchy’s theorem for Abelian groups –Automorphisms – Inner automorphism - Cayley’s theorem, permutation groups.

Definition and Examples –Some Special Classes of Rings – Commutative ring – Field –Integral domain - Homomorphisms of Rings.

Ideals and Quotient Rings – More Ideals and Quotient Rings – Maximal ideal - The field of Quotients of an Integral Domain.