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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).

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Have a look at the Numberphile video series on youtube. They have a lot of videos for non-mathematicians who are interested! – Ed_4434 8 hours ago
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Your non-mathematician friend might find the book Abel's Proof, by Peter Pesic, worth a look. – Barry Cipra 8 hours ago
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Why exactly do they want to learn about groups? If it is for an application (e.g. point group theory in inorganic chemistry) then it might be best to go for a presentation that is interlaced with the application, rather than a standard mathematical presentation. – Ian 8 hours ago
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@Ian My friend is interested on general principles (she is actually a film-maker!) – Igor Rivin 7 hours ago
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If you round to the nearest hour, people use an Abelian additive group of order $12$ or $24$ every day when working with time. That's secretly everyone's first group. – Todd Wilcox 3 hours ago
up vote 5 down vote

I recommend Marcus du Sautoy's book: Finding Moonshine : Mathematician's Journey Through Symmetry
enter image description here

He is also the author of The Music of the Primes.

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up vote 4 down vote

Try The Fascination of Groups by Budden.

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up vote 4 down vote

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.

enter image description here

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up vote 3 down vote

Two books not yet mentioned that the OP might want to consider are:

Groups in the New Mathematics by Irving Adler (1967)

Groups and Their Graphs by Israel Grossman and Wilhelm Magnus (1964)

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up vote 0 down vote

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.

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