• Singular Homology
• Computational Methods
• Cohomology and Duality
• Basic Homotopy Theory
• The Homotopy Theory of CW Complexes
• Vector Bundles and Principal Bundles
• Spectral Sequences and Serre Classes
• Characteristic Classes, Steenrod Operations, and Cobordism
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
Haynes Miller is Professor of Mathematics at the Massachusetts Institute of Technology. Past managing editor of the Bulletin of the American Mathematical Society and author of some sixty journal articles, he has directed the PhD theses of thirty students during his tenure at MIT. He is the editor of the recently published Handbook of Homotopy Theory. His visionary work in university-level education was recognized by the award of MIT's highest teaching honor, the Margaret MacVicar Fellowship.