The emergence of the first sources of light at redshifts of z ~ 10-30
signaled the transition from the simple initial state of the Universe to one of
increasing complexity. We review recent progress in our understanding of the
formation of the first stars and galaxies, starting with cosmological initial
conditions, primordial gas cooling, and subsequent collapse and fragmentation.
We emphasize the important open question of how the pristine gas was enriched
with heavy chemical elements in the wake of the first supernovae. We conclude
by discussing how the chemical abundance patterns conceivably allow us to probe
the properties of the first stars and subsequent stellar generations, and allow
us to test models of early metal enrichment.Comment: 52 pages, 20 figures, clarifications, references added, accepted for
publication in the Reviews of Modern Physic
