group theory for non-mathematicians
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.
Try The Fascination of Groups by Budden.
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.