To celebrate the coming of the new millennium, the Clay Mathematics Institute offered a $1,000,000 for the solution of each of seven mathematical problems. (If you fancy having a go at one of them, well the Poincaré conjecture has already been solved, but you might be interested in my thoughts on the P vs NP problem
) In The Millennium Problems
Keith Devlin gives an introduction to each of these problems. The book is written in a non-technical style without too much mathematics, and so is suitable for any reader who wants to get an idea of the nature of these seven problems.
My main criticism of the book is that the task Devlin has taken on is too much to fit into one book. Each chapter has a lot of introductory material, which doesn't leave much space for the description of the problem itself.. Most of the problems really need a book to themselves, such as those that have been written on the Riemann Hypothesis. For the last two chapters Devlin doesn't attempt to explain the maths leading up to the problem, he just tries to give the reader an overall feel for the problem, which in some ways is a more satisfactory way of using the space available.