  A covariant causal set (c-causet) is a causal set that is invariant under
labeling. Such causets are well-behaved and have a rigid geometry that is
determined by a sequence of positive integers called the shell sequence. We
first consider the microscopic picture. In this picture, the vertices of a
c-causet have integer labels that are unique up to a label isomorphism. This
labeling enables us to define a natural metric $d(a,b)$ between time-like
separated vertices $a$ and $b$. The time metric $d(a,b)$ results in a natural
definition of a geodesic from $a$ to $b$. It turns out that there can be $n\ge
1$ such geodesics. Letting $a$ be the origin (the big bang), we define the
curvature $K(b)$ of $b$ to be $n-1$. Assuming that particles tend to move along
geodesics, $K(b)$ gives the tendency that vertex $b$ is occupied. In this way,
the mass distribution is determined by the geometry of the c-causet. We next
consider the macroscopic picture which describes the growth process of
c-causets. We propose that this process is governed by a quantum dynamics given
by complex amplitudes. At present, these amplitudes are unknown. But if they
can be found, they will determine the (approximate) geometry of the c-causet
describing our particular universe. As an illustration, we present a simple
example of an amplitude process that may have physical relevance. We also give
a discrete analogue of Einstein's field equations.
