Abstract Algebra

Marc Hamman mentioned that category theory makes more sense once you've learned abstract algebra. Category theory is referred to frequently in the more theoretical aspects of static type systems, and so I'm interested in trying to understand it better. Therefore I'm learning about abstract algebra.

You may have heard the terms "ring" and "group". These are terms that come from abstract algebra. Here's a good introduction to the intuition behind rings, groups, and fields. After reading that introduction, I find myself strongly reminded of haskell's type classes. Type classes seem much more similar to abstract concepts like rings and groups than to OO-style polymorphism.

I'm still looking for a deeper discussion of abstract algebra and its uses. Maybe I'll end up getting a textbook or taking a class. Google found this online textbook, but it doesn't seem to have enough concrete motivations to get me to tackle it on my own. The "enrichment" section helps, but I'd prefer if the main text were written like the enrichment section.

There doesn't seem to be anything on abstract algebra in MIT's OpenCourseWare Mathematics section, either.