lecture1 (Euler characteristics and supersymmetric quantum mechanics [hand-written])
lecture2 (manifolds, tangent spaces, vector fields, tangent bundles)
lecture3 (cotangent bundles, differential forms)
lecture4 (de Rham cohomology, metric, harmonic forms, Hodge theorem, Poincare duality)
lecture5 (Riemannian geometry, Eintein equations, Gauss-Bonnet theorem)
lecture6 (homotopy, fundamental groups, homotopy groups)
lecture7 (simplicial complex, homology, Lefschetz fixed-point theorem, Poincare-Hopf theorem)
lecture8 (Lie groups, Lie algebras, vector bundles)
lecture9 (principal G-bundles, connections, curvatures, Yang-Mills action)
lecture10 (characteristic classes, Chern-Weil theory)
lecture11 (flat connections, Chern-Simons theory)
lecture12 (index theorem, Hirzebruch-Riemann-Roch theorem, anomaly, supersymmetry)
Epilogue (quantum Hall effects, this note is essentially a write-up of Witten's slides)
Extra1 (complex, Kahler, Calabi-Yau manifolds)
Extra2 (symplectic geometry, integrable system)
(These notes are written by referring to various sources without mentioning them. Comments are welcome.)
Added: There are many incorrect statements, and updated notes are available for the course in 2019.
Homework
First, you should try to solve problem sets by yourself.
If you cannot solve a problem. the corresponding solution will be sent on request.