  We describe the public release of the Cluster Monte Carlo Code (CMC) a
parallel, star-by-star $N$-body code for modeling dense star clusters. CMC
treats collisional stellar dynamics using H\'enon's method, where the
cumulative effect of many two-body encounters is statistically reproduced as a
single effective encounter between nearest-neighbor particles on a relaxation
timescale. The star-by-star approach allows for the inclusion of additional
physics, including strong gravitational three- and four-body encounters,
two-body tidal and gravitational-wave captures, mass loss in arbitrary galactic
tidal fields, and stellar evolution for both single and binary stars. The
public release of CMC is pinned directly to the COSMIC population synthesis
code, allowing dynamical star cluster simulations and population synthesis
studies to be performed using identical assumptions about the stellar physics
and initial conditions. As a demonstration, we present two examples of star
cluster modeling: first, we perform the largest ($N = 10^8$) star-by-star
$N$-body simulation of a Plummer sphere evolving to core collapse, reproducing
the expected self-similar density profile over more than 15 orders of
magnitude; second, we generate realistic models for typical globular clusters,
and we show that their dynamical evolution can produce significant numbers of
black hole mergers with masses greater than those produced from isolated binary
evolution (such as GW190521, a recently reported merger with component masses
in the pulsational pair-instability mass gap).
