A very smart non-mathematician friend is looking to learn about groups, and I was wondering if people might have suggestions (this is NOT a duplicate of this question, since a textbook is not what I am looking for, at least not at first).
Groups and Symmetry: A Guide to Discovering Mathematics, by David W. Farmer.
The highlighted title may convince that it assumes not too much mathematics for the learner. It is very little book, not of the type Definition-Theorem-Proof.
At least (in on-line preview) I don't find a single concrete mathematical statement, but always beautiful pictures and only that.
I recommend the Marcus du Sautoy's book: Finding Moonshine : Mathematician's Journey Through Symmetry
He is also the author of The Music of the Primes.
I would suggest to read, Simon Singh's Fermat's Last Theorem. http://simonsingh.net/books/fermats-last-theorem/
It starts with the introduction to simple problem, solutions. And entire history as it evolves to solve the problem surrounding group theory. And then into advanced theory.