It's a bit hard to review this book without having in mind Alex's Adventures in Numberland, published in the same year. Both books cover similar ground, although the approaches differ greatly. Whereas Alex Bellos travelled and spoke to various people who had a particular passion for certain aspects of mathematics or numbers, du Sautoy's book has the distinct feeling to it that he just sat down and wrote most of it straight out of what was in his own head. The ending of the book somewhat confirms this, as he states the book came out of his giving the Royal Institution Christmas lectures in 2006, and a few other projects he had previously worked on.
The book is broken down very simply into just 5 chapters, each with a basic premise to be looked at. But here, du Sautoy's passion for mathematics breaks through and he veers wildly off course and looks down a few sidestreets along the way. So if you pick a point about three-quarters of the way through each chapter, whatever is being discussed may not seem to have an immediate connection to what the chapter started out talking about. But this is not a criticism; merely a point of observation. It may not be to some people's liking, though I think it adds to the charm of the book.
Consistent with the philosophy of most mathematicians, du Sautoy believes that the joy in maths is to be found in doing it for oneself, not merely in the exposition of another. To this end, there are consistent puzzles inserted throughout the book for the reader to follow up on. So the fact that it doesn't take long to read cover to cover (I did it in 4 days) belies the depth of material that the pages didn't have room for and are followed up online. The book does get gradually more and more technical, which may put off some readers. Towards the end, I had to pull out a pen and some paper to follow a few of the steps.
Overall, it's written in a really down-to-earth manner with du Sautoy's enthusiasm evident on almost every single page, especially those page numbers which are prime numbers which he conveniently instructed the printers to make bold! I would recommend this for anyone interested in mathematics, though I disagree with the age ranged suggested (1-101, even if he did mean it in binary!). I think it should fairly accessible to an average 10 year old or a smart 8 year old, but with plenty to interest adult readers as well.