G. Rollet

lecture 1 I)Definition of classical integrability a)Hamiltonian systems b)the example of uncoupled harmonic oscillators, action/angle variables c)Liouville Theorem d)the example of the pendulum, Backlund transformations, solitons

lecture 2 II) the first algebraic tools a)Isospectral dynamics, Lax pair b)r-matrix c)classical Yang-Baxter equation(s)

lecture 3 III)Notion of quantum integrability a)monodromy and transfer matrices b)R-matrix and Quantum Yang-Baxter equation c)Classical limit IV)to go further