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The book develops the theory of secondary cohomology operations for singular cohomology theory. The author develops the subject 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 Massey-Peterson 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 written for graduate students and research mathematicians interested in algebraic topology and can be used for self-study or as a textbook for an advanced course on the topic.