I'm in the latter stages of my third year (of four) studying maths at university. I have to pick my modules for my fourth year, and we have the opportunity to do a project for one of our modules. This normally entails independently reading around a subject and writing a 30-40 page document that isn't too dissimilar in structure and style from the lecture notes used by our lecturers. Ideally, I would like to do a project on some branch of algebra, but wasn't sure specifically which part. So far, I've done modules in linear algebra, group theory, ring theory, representation theory, Galois theory and algebraic number theory. There's nothing stopping me doing more advanced stuff in these areas, but I also wouldn't mind doing something pretty new. It's meant to be fairly advanced, but understandable to a competent/good final year undergraduate. Has anyone got any suggestions? I'd thought about topics such as algebraic graph theory, Noetherian ring theory or Lie algebras, so if anyone could give me an opinion on some of those, it would be useful.