  This expository monograph cuts a short path from the common, elementary
background in geometry (linear algebra, vector bundles, and algebraic ideals)
to the most advanced theorems about involutive exterior differential systems:
(1) The incidence correspondence of the characteristic variety, (2) Guillemin
normal form and Quillen's thesis, (3) The Integrability of Characteristics by
Guillemin, Quillen, Sternberg, and Gabber, and (4) Yang's Hyperbolicity
Criterion. To do so, the geometric theory of PDEs is reinterpreted as the study
of smooth sub-bundles of the Grassmann bundle, whereby the rank-1 variety is
emphasized. The primary computational tool is an enhanced formulation of
Guillemin normal form that is equivalent to involutivity of tableaux.
