  A general model for geometric structures on differentiable manifolds is
obtained by deforming infinitesimal symmetries. Specifically, this model
consists of a Lie algebroid, equipped with an affine connection compatible with
the Lie algebroid structure. The curvature of this connection vanishes
precisely when the structure is locally symmetric.
  This model generalizes Cartan geometries, a substantial class, to the
intransitive case. Simple examples are surveyed and corresponding local
obstructions to symmetry are identified. These examples include foliations,
Riemannian structures, infinitesimal G-structures, symplectic and Poisson
structures.
