  It is well known that, in the first-order formalism, pure three-dimensional
gravity is just the BF theory. Similarly, four-dimensional general relativity
can be formulated as BF theory with an additional constraint term added to the
Lagrangian. In this paper we show that the same is true also for
higher-dimensional Einstein gravity: in any dimension gravity can be described
as a constrained BF theory. Moreover, in any dimension these constraints are
quadratic in the B field. After describing in details the structure of these
constraints, we scketch the ``spin foam'' quantization of these theories, which
proves to be quite similar to the spin foam quantization of general relativity
in three and four dimensions. In particular, in any dimension, we solve the
quantum constraints and find the so-called simple representations and
intertwiners. These exhibit a simple and beautiful structure that is common to
all dimensions.
