geometry of differential equations

This paper contains a survey of papers on the geometry of differential equations, which appeared no earlier than 1972, continuing the general survey (RZhMat, 1974, 11A800), and considers in more detail a special cycle of investigations of the geometry of systems of partial differential equations, distinguished by the presence of practical applications. Then we continue the survey of new results on the geometry of an ordinary differential equation of arbitrary order, started in (RZhMat, 1978, 1A645). There is constructed a general theory of invariants of equations, and classes of equations admitting a simplified coordinate representation are invariantly distinguished.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 12, pp. 127–164, 1981.