It is gratifying to learn that there is still sufficient interest in this book for it to be worth producing a new edition. Although there is a case for substantially rewriting some sections, to attempt this would have delayed production indefinitely. I am thus particularly pleased that Andrew Ranicki has supplemented the original text by notes which give hints to the reader, indicate relevant subsequent developments, and say where the reader can find accounts of such newer results. He is uniquely qualified to do this, and I am very happy with the result. The first edition appeared before the days of TfjjX, so the entire manuscript had to be re-keyed. I am grateful to Iain Rendall for doing this efficiently and extremely accurately.