Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS aims to fill that gap with the publication of this 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...