Physics

Canonical transformations, Noether's theorem, Hidden symmetry of Kepler motion, Nambu mechanics

Structure constants, Adjoint Representation of Lie algebra

Constraints, Symplectic geometry, Hamilton's equations revised

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