  This paper is based on the causal set approach to discrete quantum gravity.
We first describe a classical sequential growth process (CSGP) in which the
universe grows one element at a time in discrete steps. At each step the
process has the form of a causal set (causet) and the "completed" universe is
given by a path through a discretely growing chain of causets. We then quantize
the CSGP by forming a Hilbert space $H$ on the set of paths. The quantum
dynamics is governed by a sequence of positive operators $\rho_n$ on $H$ that
satisfy normalization and consistency conditions. The pair $(H,\brac{\rho_n})$
is called a quantum sequential growth process (QSGP). We next discuss a
concrete realization of a QSGP in terms of a natural quantum action. This gives
an amplitude process related to the sum over histories" approach to quantum
mechanics. Finally, we briefly discuss a discrete form of Einstein's field
equation and speculate how this may be employed to compare the present
framework with classical general relativity theory.
