Differentiable Manifolds

Smooth Manifolds and Embedded Submanifolds Regular Values and Level Sets Tangent Spaces and Differential Maps Immersions, Submersions, and Embeddings Transversality and Intersection Theory Sard's Theorem and Generic Transversality Vector Fields and Flows Lie Groups and Matrix Lie Groups Lie Group Actions and Homomorphisms Left-Invariant Vector Fields Tangent Bundles and Vector Bundles Orientability and Volume Forms Differential Forms and Exterior Calculus Pullbacks and Wedge Products de Rham Cohomology Compactly Supported Forms and Integration Distributions, Plane Fields, and Frobenius Integrability Homotopy and Degree on Manifolds Diffeomorphisms and Isotopy Methods Morse Theory and Critical Points Lie Algebras and Exponential Maps Stokes' Theorem and Integration on Manifolds Smooth Extension and Approximation Theorems