  First-order jet bundles can be put at the foundations of the modern geometric
approach to nonlinear PDEs, since higher-order jet bundles can be seen as
constrained iterated jet bundles. The definition of first-order jet bundles can
be given in many equivalent ways - for instance, by means of Grassmann bundles.
In this paper we generalize it by means of flag bundles, and develop the
corresponding theory for higher-oder and infinite-order jet bundles. We show
that this is a natural geometric framework for the space of Cauchy data for
nonlinear PDEs. As an example, we derive a general notion of transversality
conditions in the Calculus of Variations.
