Although the theory and applications of secondary cohomology operations are an important part of an advanced graduatelevel algebraic topology course, there are few books on the subject. The AMS fills that gap with the publication of the present volume. The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among many applications considered are the Hopf invariant one theorem (for all primes \(p\), including \(p = 2\)), Browder's theorem on higher Bockstein operations, and cohomology theory of MasseyPeterson fibrations. Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary of more advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations. The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for selfstudy or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions. Readership Graduate students and research mathematicians interested in algebraic topology. Reviews "The book contains many examples and exercises and new material not published elsewhere. This book can be warmly recommended to readers interested in homotopy theory."  Zentralblatt MATH "In all, this book gives an excellent introduction ... to a technical, but extremely important field ... This book is highly recommended for both beginners and experts."  Mathematical Reviews Table of Contents  Review of primary operations
 Segue to secondary operations
 Fundamental constructions
 Secondary cohomology operations
 Calculations with secondary operations
 The Hopf invariant
 The cohomology structure of universal examples
 Bibliography
 Index
