  The elegance of inflationary cosmology and cosmological perturbation theory
ends with the formation of the first stars and galaxies, the initial sources of
light that launched the phenomenologically rich process of cosmic reionization.
Here we review the current understanding of early star formation, emphasizing
unsolved problems and technical challenges. We begin with the first generation
of stars to form after the Big Bang and trace how they influenced subsequent
star formation. The onset of chemical enrichment coincided with a sharp
increase in the overall physical complexity of star forming systems. Ab-initio
computational treatments are just now entering the domain of the predictive and
are establishing contact with local observations of the relics of this ancient
epoch.
