An Introduction to Differential Manifolds
by Jacques Lafontaine · Lafontaine
A Springer graduate text that builds the theory of smooth manifolds from submanifolds of Euclidean space through tangent bundles, vector fields, Lie groups, differential forms, de Rham cohomology and integration, with many worked exercises for readers comfortable with multivariable calculus.
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Differential Topology
nLab: Differential Topology
The nLab wiki entry on differential topology, a collaborative reference written by working mathematicians. It frames smooth manifolds, maps and their invariants from a higher-categorical viewpoint and links outward to related concepts, useful as a map of the field.
Lectures on the Geometric Anatomy of Theoretical Physics
Explore differential topology with Frederic Schuller's "Lectures on the Geometric Anatomy of Theoretical Physics" course. Learn geometric foundations!
mathoverflow.net
MathOverflow is a Q&A platform for professional mathematicians to ask and answer research-level questions, offering in-depth discussions, problem-solving threads, and expert insights across advanced math topics, including differential topology.