  The formation of the first generations of stars at redshifts z > 15-20
signaled the transition from the simple initial state of the universe to one of
increasing complexity. We here review recent progress in understanding the
assembly process of the first galaxies, starting with cosmological initial
conditions and modelling the detailed physics of star formation. In particular,
we study the role of HD cooling in ionized primordial gas, the impact of UV
radiation produced by the first stars, and the propagation of the supernova
blast waves triggered at the end of their brief lives. We conclude by
discussing how the chemical abundance patterns observed in extremely
low-metallicity stars allow us to probe the properties of the first stars.
