Representation of finite groups, irreducible representations, complete reducibility, Schur’s lemma,
characters, orthogonality, class functions, regular representations and induced representation, the
Linear groups: Representation of the group $SU(2)$
Suggested books and references:
Etingof Pavel, Golberg Oleg, Hensel Sebastian, Liu Tiankai, Schwendner Alex, Vaintrob Dmitry, Yudovina Elena,, Introduction to representation theory. With historical interludes by Slava Gerovitch, Student Mathematical Library 59. American Mathematical Society. 2011.
J. P. Serre, Linear representations of finite groups, Graduate Texts in Mathematics. Vol. 42. Springer-Verlag. New York-Heidelberg. 1977.