Click representations_of_finite_groups.pdf link to view the file.
Representation theory of groups is a meeting ground for linear algebra and group theory. It is a window looking out on the world of algebra. This set of notes is downloaded from:
http://web.science.mq.edu.au/~chris/groups/chap07.pdf
It should give you general idea. I am sure you will like the essence of the theory. There is extensive literature on the subject.