Introduction to integrable systems I

This mini-course consists of three parts. In the first part, we will study the theory of integrable
Hamiltonian systems of hydrodynamic type. In the second part, we study perturbations of
integrable hierarchies of hydrodynamic type. In the third part, we study tau structure and the
relationship between integrable hierarchies and topology of moduli space of stable algebraic
curves (in particular Hodge integrals).