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1) groups, modules, rings - all the basic algebra stuff but for a physicist

2) topological spaces, compactness, ...

I need books for a theoretical physicist to read up on these topics so that I could study, say, algebraic topology next. Now the books needn't be too basic but being a physicist I'm not a big fan of all the finite groups, pure math stuff, so the fewer examples with tiling and such the better.

Can anyone help? Math majors are more than welcome to comment.