Utilitarian Differential Geometry 2: Vector Fields

This is the longest one of the lot because I've attempted to mention some examples.

1. Bundles and bundle sections 0:00
2. Construction of the tangent bundle: the manifold structure 6:06
3. Vector fields, smooth sections of the tangent bundle 1:24:15
4. Is the set of all vector fields a vector space? Basis and dimensionality 1:28:33
5. A cautionary tale: TR2 vs TS2 vs TT2 1:51:38
6. Pushforward map 2:13:15
7. The case of a Lie group: a global basis, application of pushforward 2:35:20
8. Covector and tensor fields, pullback map 3:07:09