We briefly survey  some  history of the exterior differential system, especially the problem raised by J. Pfaff 

in 1814 that culminates with the Frobenius theorem on integrability and the notion of  the first integral and their generalizations. 

Then we introduce degenerate Pfaffian systems with solutions that admit isolated singularities.  As an application we discuss examples of

evolution of hypersurfaces including the eikonal equations and the mean curvature flows.