Rough plan

1. Generalities on representation theory
2. Representations of S_n (Specht modules, Okounkov--Vershik approach etc)
3. Representations of SL_2(F_q) (Drinfeld curve, a little bit of Deligne--Lusztig)
4. Representations of GL_n(F_q) (Gelfand--Graev, Zelevinsky's PSH theory etc)
5*. Selected topic 1: Some characters from number theory (Legendre symbol, power residue symbol, Hilbert symbol)
6*. Selected topic 2: Stasinski--Stevens's 2017 BLMS paper.

The first part would be mainly based on Etingof et al's book and Serre's book. The remaining parts may not be in the order they appeared in the list.