The book represents a very accessible invitation to some of the essential aspects of quantum computation. While the emphasis is on the mathematical side of the subject, several of the chapters cover the connections to physics and computer science as well. The editor is also one of the authors (of several chapters in the book.--Very nice ones!) The other authors include Peter Shor(an introduction), Dan Gottesman(quantum error correction), Alex Kitaev(quantum codes), U. Vazirani(quantum complexity), and Louis Kauffman(quantum topology). The book is great both for selfstudy and for a beginning course, and it is enjoyable reading.