I second Baby Rudin. The problem sets are nearly legendary and the writing is terse. I might have to read through it again myself sometime. "Algebra" by Arti

I second Baby Rudin. The problem sets are nearly legendary and the writing is terse. I might have to read through it again myself sometime. "Algebra" by Artin is also a great choice if you want to learn about modern algebra. There's some good stuff in there for looking at linear transformations in, say, 2-space, as groups.