  We present an analytical theory for the nonlinear optical response of a
strongly interacting Rydberg gas under conditions of electromagnetically
induced transparency. Simple formulae for the third order optical
susceptibility are derived and shown to be in excellent agreement with recent
experiments. The obtained expressions reveal strong nonlinearities, which in
addition are of highly nonlocal character. This property together with enormous
strength of the Rydberg-induced nonlinearities is shown to yield a unique
laboratory platform for nonlinear wave phenomena, such as collapse-arrested
modulational instabilities in a self-defocussing medium.
