  Let (M,g) be an analytic, compact, Riemannian manifold with boundary, of
dimension n >= 2. We study a class of generalized Radon transforms, integrating
over a family of hypersurfaces embedded in M, satisfying the Bolker condition
[23]. Using analytic microlocal analysis, we prove a microlocal regularity
theorem for generalized Radon transforms on analytic manifolds defined on an
analytic family of hypersurfaces. We then show injectivity and stability for an
open, dense subset of smooth generalized Radon transforms satisfying the Bolker
condition, including the analytic ones.
