References

[FH]Fulton & Harris, Representation theory: a first course.
[Le]Ledermann, The theory of group characters.
[LJ]Liebeck & James, Representation theory of finite groups.
[J] G.D.James, The representation theory of the symmetric group
[M] I.G.Macdonald, Symmetric functions and Hall polynomials
[Et] P.Etingof and others, Introduction to representation theory,
http://arxiv.org/pdf/0901.0827.pdf
[La] S.Lang, Algebra 1965
[Lu] G.Lusztig, Affine quivers and canonical bases, Publications
Mathematiques, no 76, 1992
[Lu''] G.Lusztig, Canonical bases arising from quantized enveloping algebra, 
Jour.American Math.Society, vol.3 1990
[B] N.Bourbaki, Algebra 

Topics for a project

1) Representations of Lie algebras. Describe in detail the irreducible
representations of the Lie algebra sl(2). (See for example Humphreys' book
on Lie algebras.)
2) Representations of compact groups. Show how the results we covered for
representations of finite groups extend to compact groups. (See for example 
Ch.4 of Serre's book.)
3) Semisimple algebras. (See for example [La], Ch.17 or
[B], Ch.VIII; applications to finite groups in Serre, 6.1.)
4) Quivers and their representations (see for example [Lu''] Sec.4, or [Et].)
5) Finite subgroups of SL_2(C), Dynkin diagrams and McKay correspondence.
(See for example [Lu] Sec.1 or [Et].)
6) Overview of representation theory of a finite group over an algebraically 
closed field of characteristic p>0. (You may consult Part III of Serre's book.)
7) Overview of the representation theory of the symmetric group.
(See for example [J],[M],[Et].)
8) Overview of Brauer's theorem (See Serre, Ch.10 or [La], Ch.XVIII, Sec.10)