2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120489In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as detour complexes. This elaborates on a lecture given at the IMA Summer Programme ``Symmetries and overdetermined systems of partial differential equations''.* Proceedings of the 2006 IMA Summer Program: Symmetries and Overdetermined Systems of Partial Differential Equations. To appear in: IMA Volumes in Mathematics and its ApplicationsDifferential GeometryAnalysis of PDEs35N05, 53A30, 53A55, 17B66text