Hamiltonian reduction and rational Calogero system

In my talk I am going to give an introduction to the theory of the moment map for the Hamiltonian group action on the symplectic manifolds with the focus on Hamiltonian reduction and integrable systems. In particular, I will show how to translate symmetries of the Hamiltonian system to the first integrals using the moment map and what kind of systems we may obtain by performing such reduction. As the main example, I will demonstrate how to obtain a rational Calogero system from the free particle system on the cotangent bundle to the Lie algebra $su(n)$.