Abstract
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.
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