**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Definition of Groups, subgroups, homomorphisms, cosets, products of groups, modular arithmetic, quotient groups.
- Groups via examples: Groups acting on sets, permutation groups, matrix groups, roots of unity, operations on cosets, normality, orbit stabiliser formulae, permutation representation.
- Class equation, Sylow's Theorems, group of prime power order and groups of order 8, computations in the symmetric group.
- Semi-direct products, groups of order pq.
- Commutator subgroup, derived series and central series, solvable and nilpotent groups, structure of finite nilpotent groups.
- Jordan Holder theorem for finite groups.
- Free groups, generators and relations, examples of group presentations, free abelian groups, statement of structure theorem of finitely generated abelian groups.

Representation, group ring etc.

- Michael Artin: Algebra
- Herstein: Topics in Algebra
- J. J. Rotman: An Introduction to the Theory of Groups
- J. F. Humphreys: A Course in Group Theory
- S. Lang: Algebra
- Dummit and Foote: Abstract Algebra