The root node for Lee’s Smooth Manifolds. Some chapters are exceptionally dense and/or long (I’m looking at you, Chapter 9), so have a lot more content covered than others.
Prerequisites Review
Fundamental ODE Theorems (Existence + Uniqueness)
Smoothness of Autonomous ODE Solutions
Chapter 3
Chapter 4
A (Failed) Attempt to Generalize Rank Theorems
Chapter 6
Weak Whitney Immersion Theroem
Chapter 8
Chapter 9
Manifold Homotopies and Measures
Chapter 10
Chapter 11
Covector Fields, Pullbacks, & Basic Line Integrals
Conservative, Closed, & Exact Covector Fields
Chapter 11 Exercises (Contd. 2)
Chapter 12
Lie Derivatives of Tensor Fields
Chapter 13
Flatness of Surfaces of Revolution
Riemannian Metrics, Killing Fields, Morse Theory, etc.
Chapter 14