A Concrete Approach to Abstract Algebra by W. W. Sawyer ($6 on Amazon!)
Though it goes a bit slow at times, it is by far the simplest, most intuitive book on Abstract Algebra in existence. Written for the non-mathematician, it does a great job of teaching the subject in simple, easy-to-understand prose. I couldn't put it down!
There are also two chapters on linear algebra, leading up to the final chapters, "vectors over fields" and "fields regarded as vector-spaces".