I am interested in group theory, and bought this book under the impression that it discussed simple group theory in a way that an amateur like me would be able to understand.
I am sure this author could have written such a book, but this isn't it. It has been dumbed down far too much (I suspect at the insistence of the publisher). He avoids simple group theory terminology, so instead of writing about "how many groups there are with 27 elements", he has "how many objects there are with 27 symmetries", which isn't going to help anyone, and is going to confuse those who understand just a little of his subject matter. Yet he mentions zeta functions several times, though without any clue as to what they are.
In chapter three he states, repeatedly, that the Alhambra palace contains examples of all 17 symmetries (he means wallpaper groups); and there are pictures of some of them. I wonder why he chose not to have a page or two illustrating all 17? This would have been interesting, or at least fun to look at, for all readers, however dumb the publisher takes them to be.
The best feature of the book is not its abortive attempts to discuss mathematics, but its anecdotes about mathematicians. If these are what you want, the book is worth buying.