A while ago, I took an introductory course on group theory, but have forgotten a good deal of the material. I therefore plan on spending the weekend reproving the theorems I once understood. However, I can't find a clean, concise list of theorems which covers everything I want to prove and does so in a logical fashion. In what order should I proceed? What would make the most sense? I plan on building up to and proving the Sylow Theorems (and possibly going even a bit further?) This means I definitely want Lagrange, Cauchy and Cayley's theorems, at least.
Depending on your goal, you should explore the following:
Gallian's text, but don't buy it new otherwise you'll be wasting a lot of money for what can be found for free in
Dummit and Foote if you're interested in being a mathematician someday, and would like a textbook which goes from basic to advanced in just about every topic you could imagine in algebra.
Rotman's An Introduction to the Theory of Groups, which if you're a student at a major university, then you should have free access to it via springerlink
If you're looking to get your feet wet, but you aren't quite sure, then hit Judson's text really hard, and top it off with Conrad's expository papers (you'll notice they're referenced here quite often). http://www.math.uconn.edu/~kconrad/blurbs/