This study gives a treatment of exterior differential systems including both the general theory and various applications. Topics include a review of exterior algebra, simple exterior differential systems, the generation of integral manifolds through the solution of a succession of initial value problems, involution, linear differential systems, tableau and torsion, the characteristic variety of a differential system, prolongation, the algebra of a linear Pfaffian system, and an introduction to Spencer Theory. Much emphasis is placed on the general theory while many examples are given. This research monograph on differential geometry is intended for graduate students in mathematics and professional mathematians.
