A friend of mine, who is a high school math teacher and majored in math in college, recently asked me for a good book to read on Abstract Algebra (presumably, group theory). She is looking for something to read semi-casually, so no serious textbooks which hide intuition.
My own education largely skipped the basics. I read through Pinter in the library one afternoon, and that was pretty much it. So, can people recommend a good book on abstract algebra/groups for the casual learner?
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It depends the level of the casual reader (unless by casual you meant low prereqs). If you are looking for a book that requires a little more sophistication, but pays back two-fold in intuition I believe Artin's book Algebra is a good place to look. In particular, it helps motivate abstract groups by looking at the much more managable, understandable, notion of matrix groups.
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She will love Fearless Symmetry by Ash / Gross. Mostly group theory but that's the best start, don't you think so?
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Pinter is an excellent book, but I'd like to also recommend Abstract Algebra and Solution by Radicals, by John and Margaret Maxfield. It's very readable, and takes a semi-casual path through group theory, ending with elementary Galois theory and impossible constructions. This book was my first introduction to abstract algebra several years ago. If your friend wants a gentle introduction to the subject, I think it could be ideal.
"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.