* Mathematical Bases:
* Manifolds, Flows, Lie Groups and Lie Algebras
* Geometry of Surfaces in R3
* Riemannian Geometry
* Dynamical Systems:
* Free Rotation of a Rigid Body
* Water Waves and KdV Equation
* Hamiltonian Systems: Chaos, Integrability and Phase Transition
* Flows of Ideal Fluids:
* Gauge Principle and Variational Formulation
* Volume-Preserving Flows of an Ideal Fluid
* Motion of Vortex Filament
* Geometry of Integrable Systems:
* Geometric Interpretations of Sine-Gordon Equation
* Integrable Surfaces: Riemannian Geometry and Group Theory.