Professor Andrei is super friendly, but don't let his friendliness fool you. There are no real undergraduate courses that could prepare one for his lectures.
Understanding the representation of finite groups is necessary and insufficient. Andrei cites results/concepts in functional analysis, differential equations(more advanced than the freshman differential equations courses), algebraic topology, Riemannian geometry, and sometimes commutative algebra/algebraic geometry in his lectures. A classmate told me that he watched Andrei's lectures three/four times and what Andrei said started to sink in. I didn't have the time or the ingenuity to do that, so I ended up not understanding most of his lectures. If you are neither well-prepared nor mathematically mature, don't take Andrei's course!