Formation of the First Stars

How and when did the first generation of stars form at the end of the cosmic dark ages? Quite generically, within variants of the cold dark matter model of cosmological structure formation, the first sources of light are expected to form in ~ 10^{6} M_sun dark matter potential wells at redshifts z > 20. I discuss the physical processes that govern the formation of the first stars. These so-called Population~III stars are predicted to be predominantly very massive, and to have contributed significantly to the early reionization of the intergalactic medium. Such an early reionization epoch is inferred from the recent measurement of the Thomson optical depth by the {\it WMAP} satellite. I address the importance of heavy elements in bringing about the transition from an early star formation mode dominated by massive stars, to the familiar mode dominated by low mass stars, at later times, and present possible observational probes. This transition could have been gradual, giving rise to an intermediate-mass population of still virtually metal-free stars (``Population II.5''). These stars could have given rise to the peculiar class of black-hole forming supernovae inferred from the abundance pattern of extremely iron-poor stars.