What is the best way to understand abstract algebra? Any good resources? I'm studying and studying and still not understanding.

What specifically are you having problems with?

I'm having problems knowing how and where to start writing a proof. Are there tricks to the trade? For example, what proof would you write for the question below and why?
Thanks in advance.


Let V be the direct sum of the R-modules V1, Vn, and let W be the direct sum of
R-modules W1, Wm. Indicate how a module homomorphism from V to W can be
represented by a matrix. (The entries of the matrix need not be elements of R.)