Symplectic Geometry

This lecture covers the background on symplectic geometry, focusing on symplectic manifolds, canonical symplectic structures, tautological 1-forms, and symplectic vector fields. The content includes Darboux theorems, symplectic forms, volume forms, and Lie derivatives. The lecture also delves into symplectic manifolds' properties, such as closed 2-forms and preserving symplectic structures under different transformations.