This talk presents k-contact geometry as an extension of contact geometry to the study of PDEs. We first introduce its distributional formulation via k-contact distributions and discuss k-contact isotropic, Legendrian, and coisotropic submanifolds, together with higher-order polarisations and, in particular, polarisations of jet type.

We then show that the Cartan distribution of every finite-order jet bundle is naturally a k-contact distribution, with k determined by the jet order and the dimensions of the underlying fibre bundle. A local recognition theorem characterises when a k-contact distribution is locally equivalent to the Cartan distribution of a finite-order jet bundle. This framework provides a geometric setting for constructions involving different jet bundles and, in certain cases, allows non-local structures to be studied without passing to infinite-order jets. Applications include lambda-symmetries and other new and known non-local symmetries, as well as reduction techniques for PDEs that place several non-local reductions and their generalisations within a common geometric framework.