  An overview of some recent results on the geometry of partial differential
equations in application to integrable systems is given. Lagrangian and
Hamiltonian formalism both in the free case (on the space of infinite jets) and
with constraints (on a PDE) are discussed. Analogs of tangent and cotangent
bundles to a differential equation are introduced and the variational Schouten
bracket is defined. General theoretical constructions are illustrated by a
series of examples.
