  We discuss a recurrent geometrical method, due to \'Elie Cartan and von Weber
([1],[11]) enabling us to determine, step by step, the maximal integral
manifolds of a not necessarily integrable nor regular Pfaffian system. The
dimensions of such integral manifolds can, of course, vary from point to point
but more so can vary at a given point it depending upon the choice of their
recurrent buildup. When the system is regular and integrable then, of course,
we obtain the maximal integral leaves of the integral foliation. Attention is
also given to those integrable systems that can be integrated by quadratures
which was, in the 19th century, the dream of many. However, our main interest
resides in enhancing the Jordan-H\"older integration procedure so as to
construct the local maximal integral manifolds that find many applications.
