- Introduction to multilinear algebra, tensor algebra, symmetric algebra and exterior algebra.
- Representations and basic examples, direct sum and tensor product of representations.
- Irreducible representations, complete reducibility and Maschke's theorem, Schur's lemma.
- Character theory of representations, orthogonality relations, decomposition of the regular representation.
- Character tables of Abelian, dihedral and small groups.
- Dimension theorem, Burnside's -theorem.
- Restriction of a representation, induced representations, Frobenius reciprocity, Mackey's irreducibility criterion.
- Representation theory of symmetric groups.

- Benjamin Steinberg, Representation Theory of Finite Groups, Springer (Universitext), 2012.
- Gordon James and Martin Liebeck, Representations and Characters of Groups, Cambridge University Press, 2001.

- William Fulton and Joe Harris, Representation Theory: A First Course, Springer (Graduate Texts in Mathematics 129), 1991.
- Jean-Pierre Serre, Linear Representations of Finite Groups, Springer (Graduate Texts in Mathematics 42), 1977.