Math Stack Exchange: Tangent Space Discussions
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Math Stack Exchange's tangent-spaces tag, holding roughly 650 questions on defining tangent vectors, derivations versus curves, the differential of a smooth map, and tangent bundles. Useful for resolving specific confusions while working through a differential geometry course.
More resources on Tangent Spaces
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab: Tangent Space
Comprehensive reference with category theory perspective, linked in advanced Reddit discussions
Lectures on the Geometric Anatomy of Theoretical Physics
Learn geometric anatomy for theoretical physics with Frederic Schuller! This course explores tangent-spaces and more.
nLab
Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.