  Integral geometry deals with those integral transforms which associate to
``functions'' on a manifold their integrals along submanifolds parameterized by
another manifold. Basic problems in this context are range
characterization--where systems of PDE appear--and inversion formulae. As we
pointed out in a series of joint papers with Pierre Schapira, the language of
sheaves and D-modules provides both a natural framework and powerful tools for
the study of such problems. In particular, it provides a general adjunction
formula which is a sort of archetypical theorem in integral geometry. Focusing
on range characterization, we illustrate this approach with a discussion of the
Radon transform, in some of its manifold manifestations.
