  The Local Group (LG) is an environment accessible to detailed studies of
galaxy formation, providing a complement to the early universe. In particular,
spectroscopy of resolved stellar populations in the LG provides kinematical and
chemical information for individual stars that can be used to infer the history
of $L_\star$ galaxies like the Milky Way (MW) and Andromeda (M31). The Gaia
revolution in the MW has enabled comprehensive observational studies of the
MW's formation history. The exquisite detail in which the MW has been studied
is currently not achievable in any other $L_\star$ galaxy. For this reason, the
MW is a template for our understanding of galaxy formation. M31 is the only
external galaxy that we can currently hope study in a level of detail
approaching the MW. Studies of M31 have recently taken on greater significance,
given the growing body of evidence that its formation history differs
substantially from that of the MW. In an era of limited information about
elemental abundances in M31, I have developed a technique to apply spectral
synthesis to low-resolution stellar spectroscopy in order to measure abundances
for individual giant stars in distant LG galaxies. Through undertaking the
largest deep, spectroscopic survey of M31 to date with my collaborators, this
has resulted in the first measurements of the elemental abundances in the inner
stellar halo and stellar disk of M31, and the largest homogeneous catalog of
elemental abundances in M31. With this foundational work, we have opened the
doors to detailed studies of the chemical composition of M31. Now, we can begin
to ask--and answer--what differences in the elemental abundances of the M31 and
the MW imply for our knowledge of galaxy formation in the broader universe.
