  A nonpertubative approach to quantum gravity using precanonical field
quantization originating from the covariant De Donder-Weyl Hamiltonian
formulation which treats space and time variables on equal footing is
presented. A generally covariant ``multi-temporal'' generalized Schroedinger
equation on the finite dimensional space of metric and space-time variables is
obtained. An important ingredient of the formulation is the ``bootstrap
condition'' which introduces a classical space-time geometry as an approximate
concept emerging as the quantum average in a self-consistent with the
underlying quantum dynamics manner. An independence of the theory from an
arbitrarily fixed background is ensured in this way. The prospects and unsolved
problems of precanonical quantization of gravity are outlined.
