I will introduce the framework for studying nonlinear second
order differential equations based on the concept of Lagrangian
Grassmanian. Lagrangian Grassmanian is the manifold of all n-dimensional
vector subspaces of a 2n-dimensional symplectic space such that
symplectic form vanishes on them. In particular I will discuss the case
n=2, especially Monge-Ampére equation and its characteristics.