Marc Notes:
Originally published: New York: Harper & Row Publishers, 1968.; Includes bibliographical references (p. 207-211) and index.

Table of Contents:
Preface1. Introduction to cohomology operations2. Construction of the Steenrod squares3. Properties of the squares4. Application: the Hopf invariant5. Application: vector fields on spheres6. The Steenrod algebra7. Exact couples and spectral sequences8. Fibre spaces9. Cohomology of K(pi, n)10. Classes of Abelian groups11. More about fiber spaces12. Applications: some homotopy groups of spheres13. n-Type and Postnikov systems14. Mapping sequences and homotopy classification15. Properties of the stable range16. Higher cohomology operations17. Compositions in the stable homotopy of spheres18. The Adams spectral sequenceBibliographyIndex

Publisher Marketing:
Cohomology operations are at the center of a major area of activity in algebraic topology. This technique for supplementing and enriching the algebraic structure of the cohomology ring has been instrumental to important progress in general homotopy theory and in specific geometric applications. For both theoretical and practical reasons, the formal properties of families of operations have received extensive analysis.
This text focuses on the single most important sort of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. In the later chapters, the authors place special emphasis on calculations in the stable range. The text provides an introduction to methods of Serre, Toda, and Adams, and carries out some detailed computations. Prerequisites include a solid background in cohomology theory and some acquaintance with homotopy groups.