Astrophysical observations currently provide the only robust, empirical
measurements of dark matter. In the coming decade, astrophysical observations
will guide other experimental efforts, while simultaneously probing unique
regions of dark matter parameter space. This white paper summarizes
astrophysical observations that can constrain the fundamental physics of dark
matter in the era of LSST. We describe how astrophysical observations will
inform our understanding of the fundamental properties of dark matter, such as
particle mass, self-interaction strength, non-gravitational interactions with
the Standard Model, and compact object abundances. Additionally, we highlight
theoretical work and experimental/observational facilities that will complement
LSST to strengthen our understanding of the fundamental characteristics of dark
matter.