Casual book on abstract algebra
"A Book on Abstract Algebra" by Charles Pinter is a great book for the casual reader. It's an easy read yet maintains rigour throughout all of the topics discussed.
She will love Fearless Symmetry by Ash / Gross. Mostly group theory but that's the best start, don't you think so?
- http://books.google.com/books?id=h7oUr88S7JQC&lpg=PP1&pg=PP1#v=onepage&q&f=false
A gentle introductory book full of intuition on group theory is Nathan Carter's Visual Group Theory. This answer is doubtless much too late for the OP, but may help others looking for casual books on abstract algebra.