Chris, thank you for the reply. I have taken linear algebra and number theory and am very excited to tackle the enigmatic "abstract algebra" and all its mysteries.
I will be taking an introductory course in modern algebra this fall and wanted to build a foundation before the class began. So far I have started reading Rotman's 'introduction to theory of groups' and a few other introductory texts, but, having no experience from which to evaluate the books, I figured asking you, someone experienced with algebra, would be a good idea. I downloaded Artin's book and am having fun with the matrix approach so far.
I think I remember you saying that you study math at the graduate level. What does research in pure mathematics look like? I find it difficult to visualize a "day in the lab" for a researching pure mathematician and would like to hear what it's like for you!