In this monograph the authors redevelop the theory systematically
using two different approaches. A general mechanism for the
deformation of structures on manifolds was developed by Donald
Spencer ten years ago. A new version of that theory, based on the
differential calculus in the analytic spaces of Grothendieck, was
recently given by B. Malgrange. The first approach adopts
Malgrange's idea in defining jet sheaves and linear operators,
although the brackets and the non-linear theory arc treated in an
essentially different manner. The second approach is based on the
theory of derivations, and its relationship to the first is clearly
explained. The introduction describes examples of Lie equations and
known integrability theorems, and gives applications of the theory
to be developed in the following chapters and in the subsequent
volume.
General
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