The goal of this school is to explain several methods and result from modern Riemannian and symplectic geometry and from Hamiltonian systems, and to use them to study old problems in celestial mechanics. Among the tools are symplectic embeddings by elementary and less elementary methods, J-holomorphic curves, and systolic inequalities in Riemannien, contact and symplectic geometry. We shall apply these tools to study very explicit problems on the motion of Moon, Earth, and Sun in the form of the restricted 3-body problem and several of its limits.
