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Elementary group theory e.g. normal subgroups and quotient groups, isomorphism theorems, group actions. Elementary ring theory, e.g. ideals, polynomial rings. Basic representation theory, e.g. characters. Differential geometry, e.g. basic properties of manifolds, Lie groups, curvature and connections, elementary properties of Lie algebras.

I'm looking to learn about:

More advanced group theory, e.g. Sylow theorems, simple groups. More advanced commutative algebra and theory of ideals, perhaps Noetherian rings? More about modules as a generalization of vector spaces. Group rings and connection to representation theory. Galois theory, number fields, more representation theory.

If any of it can be tied in to equivariant dynamical systems (i.e. symmetric dynamics) then that would be great as that's what I'm doing my PhD in! Thanks a lot. :)