Report on the absolute differential equations I

Abstract

The article provides a modest survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theory in the Bourbaki sense with its own concepts and technical tools follows. In particular the external, internal, generalized and higher-order symmetries and infinitesimal symmetries together with the E. Cartan's prolongations, various characteristics, the involutivity and the controllability structures are clarified in genuinely coordinate-free terms without any use of the common jet mechanisms.