  We study deformations of Lie groupoids by means of the cohomology which
controls them. This cohomology turns out to provide an intrinsic model for the
cohomology of a Lie groupoid with values in its adjoint representation. We
prove several fundamental properties of the deformation cohomology including
Morita invariance, a van Est theorem, and a vanishing result in the proper
case. Combined with Moser's deformation arguments for groupoids, we obtain
several rigidity and normal form results.
