Michael A. Hill is Professor at the University of California, Los Angeles. He is the author of several papers on algebraic topology and is an editor for journals including Mathematische Zeitschrift and Transactions of the American Mathematical Society.

1. Introduction; Part I. The Categorical Tool Box: 2. Some Categorical Tools; 3. Enriched Category Theory; 4. Quillen's Theory of Model Categories; 5. Model Category Theory Since Quillen; 6. Bousfield Localization; Part II. Setting Up Equivariant Stable Homotopy Theory: 7. Spectra and Stable Homotopy Theory; 8. Equivariant Homotopy Theory; 9. Orthogonal G-spectra; 10. Multiplicative Properties of G-spectra; Part III. Proving the Kervaire Invariant Theorem: 11. The Slice Filtration and Slice Spectral Sequence; 12. The Construction and Properties of $MU_{\R}$; 13. The Proofs of the Gap, Periodicity and Detection Theorems; References; Table of Notation; Index.