This is a review note for reviewing Characteristic class.
I mainly use
Milnor, J. W., & Stasheff, J. D. (1974). Characteristic Classes (Revised and modernized edition by TeXromancers). Typeset by TeXromancers. Available from: Aareyan Manzoor’s website. Aareyan Manzoor’s website
Equivalence between Embedded and Abstract Manifold
Tangent Vector, Tangent Space, and Tangent Bundle
Cross-Section of Vector Bundle
Tautological Line Bundle is non trivial
Bundle with Metric and Definition