I'm slowly beginning a student of certain higher mathematics.
I'm trying to see if I would prefer to study Group Theory or Abstract Algebra.
I know that Abstract Algebra seems to "come before" Group Theory, in the sence that one usually learns the terminology of GT through AA.
Am I correct in thinking that AA is essentially a broader version of GT, whereas GT seems to just focus on rings and fields?
I'm basically trying to learn one of the two that will best lead to lie algebra(s), and get a pure math balance to differential geometry that I'm trying to learn now.
No-one can give you useful advice on what courses to take without knowing the actual content of those courses. Your best bet is to ask someone at your institution, who'll know best what's involved.