  This is the first part of a series of papers. The whole series aims to
develop the tools for the study of all almost Hermitian symmetric structures in
a unified way. In particular, methods for the construction of invariant
operators, their classification and the study of their properties will be
worked out. In this paper we present the invariant differentiation with respect
to a Cartan connection and we expand the differentials in the terms of the
underlying linear connections belonging to the structures in question. Then we
discuss the holonomic and non-holonomic jet extensions and we suggest methods
for the construction of invariant operators.
