I'm an undergraduate student studying my 4th semester of pure mathematics and I already have passed two courses in analysis that covers chapters 1 to 8 of Rudin's mathematical analysis and I've taken a course in abstract algebra that covers basics of group theory (excluding Silow's theorem) and basics of ring and module theory (including Tensor product over modules and injective, projective and flat modules). I've talked to two of my university professors to join their classes and they've agreed. I got these choices to join: 1- Finite groups theory 2- Functional algebra 3- Manifold I 4- Algebraic varieties and Riemannian manifolds 5- Real Analysis I 6- Banach algebra 7- Operator theory I'm thinking of joining two of these classes as a guest student but I'm a bit confused. I personally like algebra and geometry very much, but I don't know which one of these courses I could join. Your suggestions will be highly appreciated.