Symplectic Geometry is a meeting point for several disciplines in Science. The topic "Integrable Hamiltonian Systems" plays a central role in Symplectic Geometry and its study is being developed using a wide range of techniques in Pure and Applied Mathematics. The goal of this Euro Summer School is two- fold: on the one hand, some classical results in Integrable Systems will be revisited and on the other Hamiltonian torus actions, which stand for symmetries of the system, and their relationship with the classical results will be presented.
Integrable Hamiltonian Systems will be firstly studied under some regularity assumptions and then studied at the singular level. At this stage, some up-to-date results of singular Hamiltonian Systems will also be outlined.
The proposed Summer School consists on the three main courses: "Background of Regular Integrable Systems", "Hamiltonian torus actions and the Convexity Theorem", and "Singular Reduction and Singular Levels of the Moment Map". These courses jointly with selected talks of some experts will be the nucleus of this Euro Summer School.