Class 01 - Manifolds and smooth maps (01/16/19)

Class 02 - Tangent vectors and orientability (01/23/19)

Class 03 - Vector bundles (01/28/19)

Class 04 - Sections and tensor bundles (02/01/19)

Class 05 - Important sections: vector fields and tensor fields (02/04/19)

Class 06 - Riemannian metrics (02/06/19)

Class 07 - Volume form and integration; Connections on Vector bundles (02/11/19)

Class 08 - Connections on Vector bundles (02/13/19)

Class 09 - Riemannian connections and geodesics (02/18/19)

Class 10 - The exponential map (02/20/19)

Class 11 - Variations of curves (02/25/19)

Class 12 - Geodesics locally minimize, I (02/27/19)

Class 13 - Geodesics locally minimize, II (03/04/19)

Class 14 - Complete manifolds: Hopf Rinow-Theorem (03/06/19)

Class 15 - Curvature, I (03/18/19)

Class 16 - Curvature, II (03/20/19)

Class 17 - Jacobi fields, I (03/25/19)

Class 18 - Jacobi fields, II (03/27/19)

Class 19 - Conjugate points (03/29/19)

Class 20 - Norms of Jacobi fields, and Cartan-Hadamard Theorem (04/01/19)

Class 21 - Variations of Energy (04/03/19)

Class 22 - First/Second Variation of Energy formulas (04/08/19)

Class 23 - Topological obstructions to curvature (04/12/19)

Class 24 - Isometric Immersions (04/15/19)

Class 25 - The fundamental equations (04/17/19)

Class 26 - Curvature and submanifolds (04/24/19)

Class 27 - (04/29/19)

Class 28 - (05/01/19)