  We introduce a discrete 4-dimensional module over the integers that appears
to have maximal symmetry. By adjoining the usual Minkowski distance, we obtain
a discrete 4-dimensional Minkowski space. Forming universe histories in this
space and employing the standard causal order, the histories become causal
sets. These causal sets increase in size rapidly and describe an inflationary
period for the early universe. We next consider the symmetry group $G$ for the
module. We show that $G$ has order 24 and we construct its group table. In a
sense $G$ is a discrete approximation to the Lorentz group. However, we note
that it contains no boosts and is essentially a rotation group. Unitary
representations of $G$ are constructed. The energy-momentum space dual to the
discrete module is obtained and a quantum formalism is derived. A discrete Fock
space is introduced on this structure and free quantum fields are considered.
Finally, we take the first step in a study of interacting quantum fields.
