The first half of the course is devoted to 'classical' symplectic geometry: Lagrangians, Legendre transformations, Hamiltonians, symplectic manifolds and the Darboux-Weinstein theorem, symmetries and conservation laws and the Arnold- Liouville theorem, momentum mappings, reduction, and convexity. The second half of the course is devoted to developing elliptic methods: pseudo-holomorphic curves, Gromov compactness and moduli, applications to packing and (non)-squeezing theorems, etc. If time permits, I'll try to describe some more recent developments in Gromov-Witten theory.