Lectures on Algebraic Topology / Haynes Miller

1. Singular Homology 2. Computational Methods 3. Cohomology and Duality 4. Basic Homotopy Theory 5. The Homotopy Theory of CW Complexes 6. Vector Bundles and Principal Bundles 7. Spectral Sequences and Serre Classes 8. 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.