See our review of the second edition. The new edition has been completely revised and reorganized. A new chapter 16, on the bridge number, was added. It includes a proof of H. Schubert's theorem saying that the bridge number minus 1 is additive. The authors have reduced the number of tables given in the back of the book, reasoning that today such data is best found online, for example at the Knot Atlas, Knot Info, and Link Info sites.