Motivated by the study of symplectic Lie algebroids, we
study a describe a type of algebroid (called an E-tangent bundle) which
is particularly well-suited to study of singular differential forms and
their cohomology. This setting generalizes the study of b-symplectic
manifolds, foliated manifolds, and a wide class of Poisson manifolds.
We generalize Moser's theorem to this setting, and use it to construct
symplectomorphisms between singular symplectic forms. We give appli-
cations of this machinery (including the study of Poisson cohomology),
and study specific examples of a few of them in depth.Preprin
