Symplectic and Contact Geometry of Monge–Ampere equation: Introduction and application

I am going to present an introduction into the geometric approach to Monge–Ampere operators and equations based on contact and symplectic structures of cotangent and the 1st jet bundles of a smooth manifold. This approach was developed by V. Lychagin and goes back to the ideas of E. Cartan and his successor T. Lepage. I shall try to make my talk self-contained. I also plan to discuss various applications and links with important geometric structures.