Physics

From quantum mechanics to Lie groups, Representation of groups, Important Lie group examples

Hamilton-Jacobi theory, Integrable  systems

Group, subgroup, coset, normal subgroup, direct product group, semi-direct product group, quotient group 

Review of Lagrangian mechanics: Action principle, Integrals of motion, Noether's theorem

Introduction to differential geometry: Lie derivative and differential forms

Introduction to differential geometry: manifolds and tensors