This is an exceptionally well-written book on why there are strong reasons for people to become "many worlders", accepting that multiple versions of themselves are branching into overlapping existence as the results of the escalation of quantum microscopic events. This philosophical outlook is shocking on many levels, and initially strikes people as absurd, but the reasons reviewed in this fine book should start to make people more open-minded to its possible reality.
The "Many worlds" idea initially arose from people trying to make sense of the philosophical issues of quantum mechanics. However it turns out that the really problematic issues arise, not from quantum mechanics itself, but from some celebrated experiments that have been carried out (by Alain Aspect and others), verifying what's known as the Bell Inequalities for spatially separated particles originating from a common origin. These experiments cry out for an explanation, independent of whatever mathematical formalism (quantum mechanics or anything else) is used to calculate the bafflingly strong statistical correlations observed in the results. As the book makes clear, there really is no easy solution to this problem.
The author has a pleasant writing style, mixing in detective story writing and references to science fiction stories, with analysis of philosophical ideas. There's no complex maths to surmount - though the reader will have to think carefully, going through various passages. (The effort is worth it!)
Unlike many books which seem to repeat the same few themes spread over many chapters, each chapter in this book introduces important new concepts - which is another reason why it's rewarding to read it.
It's a shame the book isn't better known. As I write this, the current edition of the Scientific American (Dec 2007) has a pretty good article in it, on the subject of the many worlds interpretation. The article commemorates the 50th anniversary of this interpretation first appearing in print - in the doctoral thesis of Hugh Everett III. The SciAm article lists some useful pointers to further reading - including "The Fabric of Reality" by David Deutsch, which is another book that I thoroughly recommend. But alas, there's no mention of Colin Bruce's book.