What are the different parts in Abstract Algebra? For example Algebraic Geometry, Algebraic Number theory, Universal algebra, Category theory and so on, can all these subjects be categorized? I'm a second year math student, and I need to do a presentation for other second year student, and I need to tell something about algebra and which different fields there are in abstract algebra. Because I haven't studied any of those fields that I read, I find it hard to see how you could divide all the parts of algebra.
I'm trying to let it make sense to myself. I would say that in abstract algebra, you study algebraic structures like groups, rings, algebra's. And if I inteprete @Matt Pressland correctly, you could use those algebraic structures to solve problems in geometry, number theory and topology etc. I don't understand how representation theory, Universal algebra, Category theory fits in this picture.