ocw.mit.edu
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MIT OpenCourseWare (OCW) provides free, openly available course materials from MIT across disciplines. It includes lecture notes, problem sets, exams, and sometimes video lectures for many courses, including mathematics topics on manifolds, differential geometry, and topology.
More resources on Manifolds
mathworld.wolfram.com
MathWorld is an extensive online mathematical encyclopedia by Wolfram that provides thorough, well-structured articles on topics across mathematics, including manifolds. Each entry offers definitions, theorems, formulas, examples, and diagrams, with links to related concepts for deeper study.
Differential Topology
Differential Topology - A book resource
Topology from the Differentiable Viewpoint
Topology from the Differentiable Viewpoint - A book resource
ncatlab.org
nLab is a collaborative, wiki-style knowledge base for mathematics, logic, and foundations, with a special emphasis on category theory and higher structures. It offers extensive articles, definitions, and discussions on manifolds, differential geometry, topology, homotopy theory, and related topics.