- Representations of Finite Groups : Definitions, Schurs theorem, characters, induced representation and restrictions, group algebra, representations in positive characteristic, representation of symmetric groups, Young's tableaux, character formulas, Schur functors.
- Lie Groups and Lie Algebras : Definitions, exponential map, semi-simple Lie algebras, representations of $SL_n(\mathbb C), GL_n(\mathbb C)$, representations of $sl_2(\mathbb C).$
- Classifications of Complex Simple Lie Algebras : The classification theorem, root system, Dynkin diagrams, associating an algebra with a diagram, classifying all simple Dynkin diagrams.
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