Books
[CiEl12] — PDF
W. Fulton, Algebraic Topology: A First Course
E. Spanier, Algebraic Topology
M. Greenberg and J. Harper, Algebraic Topology: A First Course
Notes
Mike Usher, Math 8210 Differential Geometry lecture notes, Fall 2011 — smooth-manifold course notes covering coordinate-free tangent vectors and vector fields, partitions of unity, tangent and cotangent bundles, differential forms and exterior differentiation, submanifolds and tubular neighborhoods, flows and Lie derivatives, Cartan’s formula, and Moser’s method.
J.J. Duistermaat, Symplectic Geometry, Utrecht Spring School 2004 — lecture notes on symplectic linear algebra, symplectic manifolds and reduction, Hamiltonian systems and Poisson geometry, and Hamilton–Jacobi theory. Each of the four chapters ends with an exercise section.
Robert L. Bryant, An Introduction to Lie Groups and Symplectic Geometry (1991 lectures; revised 2018) — nine-lecture Regional Geometry Institute course notes covering symmetry and differential equations, Lie groups and group actions, symmetries and conservation laws, symplectic manifolds, classical and modern reduction, and the Gromov school of symplectic geometry. Exercise Sets 2–9 are integrated into the lecture text, with hints.
Cambridge Part II algebraic topology notes
Beckham Myers, notes on Denis Auroux’s Harvard Math 131: Introduction to Topology (Fall 2019) — lecture notes following Munkres, from metric and topological spaces, products, connectedness, compactness, countability and separation axioms, Urysohn’s lemma and metrization, through homotopy, the fundamental group, covering spaces, the Brouwer and Borsuk–Ulam theorems, universal covers and the Seifert–van Kampen theorem.
Si Li, Introduction to Algebraic Topology, Tsinghua University, Spring 2018 — expository course notes in 28 sections covering categories and functors, fundamental groupoids, coverings and fibrations, van Kampen, homotopy groups and Puppe sequences, CW complexes, singular and cellular homology, cohomology and products, Poincaré duality, spectral sequences, obstruction theory, Hurewicz, and the Eilenberg–Steenrod axioms.
Perutz, Algebraic Topology I, Fall 2008
Math 872 Algebraic Topology course contents and theorem/topic outline, Spring 2014
Math 871 exam review sheets, Fall 2013
Math 871 course contents and theorem/topic outline
Separation and countability definitions
Kriz’s algebraic topology course page (Michigan)