ocw.mit.edu
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MIT OpenCourseWare (OCW) provides free, online access to course materials from MIT classes. It includes lecture notes, assignments, exams, syllabi, and often video lectures and readings across a broad range of subjects, including mathematics.
More resources on Tangent Spaces
mathworld.wolfram.com
MathWorld is a comprehensive online mathematics encyclopedia from Wolfram Research, offering in-depth articles on a wide range of math topics. Each entry includes definitions, theorems, formulas, figures, and examples with cross-references, making it a solid resource for topics like tangent spaces.
ncatlab.org
nCatLab is a comprehensive, community-edited online encyclopedia for category theory and its applications, offering formal definitions, explanations, examples, and references. It includes topics like tangent spaces and tangent categories, connecting differential geometry with higher-category theory.