  Stars, and collections of stars, encode rich signatures of stellar physics
and galaxy evolution. With properties influenced by both their environment and
intrinsic nature, stars retain information about astrophysical phenomena that
are not otherwise directly observable. In the time-domain, the observed
brightness variability of a star can be used to investigate physical processes
occurring at the stellar surface and in the stellar interior. On a galactic
scale, the properties of stars, including chemical abundances and stellar ages,
serve as a multi-dimensional record of the origin of the galaxy. In the Milky
Way, together with orbital properties, this informs the details of the
evolution of our Galaxy since its formation. Extending beyond the Local Group,
the attributes of unresolved stellar populations allow us to study the
diversity of galaxies in the Universe.
  By examining the properties of stars, and how they vary across a range of
spatial and temporal scales, this Dissertation connects the information
residing within stars to global processes in galactic formation and evolution.
We develop new approaches to determine stellar properties, including rotation
and surface gravity, from the variability that we directly observe. We offer
new insight into the chemical enrichment history of the Milky Way, tracing
different stellar explosions that capture billions of years of evolution. We
advance knowledge and understanding of how stars and galaxies are linked, by
examining differences in the initial stellar mass distributions comprising
galaxies, as they form. In building up this knowledge, we highlight current
tensions between data and theory. By synthesizing numerical simulations, large
observational data sets, and machine learning techniques, this work makes
valuable methodological contributions to maximize insights from diverse
ensembles of current and future stellar observations.
