Abstract: In the first billion years of the universe, the first stars and galaxies formed in the smallest dark matter halos, produced high-energy photons that reionized the intergalactic medium, and polluted the universe with the first heavy elements. This early era can be accessed observationally using nearby relic stars and galaxies that have survived from ancient times. The elemental abundances of these old, metal-poor stars encode otherwise inaccessible information about the first stellar populations and the first galaxy formation histories. In this talk, I will use elements synthesized in core-collapse supernovae to learn about properties of the first stars, and elements synthesized in the rapid neutron-capture process to trace the formation of the smallest galaxies. These types of studies enable a remarkably detailed reconstruction of the early universe, which will continue to expand as we enter the era of industrial stellar spectroscopy and extremely large telescopes.