  The early chemical evolution of the Galaxy and the Universe is vital to our
understanding of a host of astrophysical phenomena. Since the most metal-poor
Galactic stars (with metallicities down to [Fe/H]\sim-5.5) are relics from the
high-redshift Universe, they probe the chemical and dynamical conditions of the
Milky Way and the origin and evolution of the elements through nucleosynthesis.
They also provide constraints on the nature of the first stars, their
associated supernovae and initial mass function, and early star and galaxy
formation. The Milky Way's dwarf satellites contain a large fraction (~30%) of
the known most metal-poor stars that have chemical abundances that closely
resemble those of equivalent halo stars. This suggests that chemical evolution
may be universal, at least at early times, and that it is driven by massive,
energetic SNe. Some of these surviving, ultra-faint systems may show the
signature of just one such PopIII star; they may even be surviving first
galaxies. Early analogs of the surviving dwarfs may thus have played an
important role in the assembly of the old Galactic halo whose formation can now
be studied with stellar chemistry. Following the cosmic evolution of small
halos in simulations of structure formation enables tracing the cosmological
origin of the most metal-poor stars in the halo and dwarf galaxies. Together
with future observations and additional modeling, many of these issues,
including the reionization history of the Milky Way, may be constrained this
way. The chapter concludes with an outlook about upcoming observational
challenges and ways forward is to use metal-poor stars to constrain theoretical
studies.
