*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii*CHAPTER I. Axiomatic Development of the Steenrod Algebra, pg. 1*CHAPTER II. The Dual of the Algebra, pg. 16*CHARTER III. Embeddings of Spaces in Spheres, pg. 30*CHAPTER IV. The Cohomology of Classical Groups and Stiefel Manifolds., pg. 37*CHAPTER V. Equivariant Cohomology, pg. 58*CHAPTER VI. Axiomatic Development of the Algebra, pg. 76*CHAPTER VII. Construction of the Reduced Powers, pg. 97*CHAPTER VIII. Relations of Adem and the Uniqueness Theorem, pg. 115*APPENDIX: Algebraic Derivations of Certain Properties of the Steenrod Algebra, pg. 133*Index, pg. 139*Errata for the Annals Study No. 50, pg. 141