  Cosmic structure originated from minute density perturbations in an almost
homogeneous universe. The first stars are believed to be very massive and
luminous, providing the first ionizing radiation and heavy elements to the
universe and forming 100 million years after the Big Bang. The impact from
primordial stellar radiation is far reaching and affects subsequent star and
galaxy formation. In this thesis, we present results from adaptive mesh
refinement calculations of the formation of the first galaxies. We gradually
introduce important physical processes, such as molecular hydrogen cooling and
stellar feedback, to base models that only consider atomic hydrogen and helium
cooling. In these base models, we find that gas in dark matter halos with
masses ~10^8 solar masses centrally collapse before multiple fragmentation
occurs in a global disc. We then investigate the importance of molecular
hydrogen cooling in early structure formation in the presence of a soft
ultraviolet radiation background. We find that molecular hydrogen plays an
important role in star formation in halos well below a virial temperature of
10,000 K even in the most extreme assumptions of negative radiative feedback.
We also present results from the first radiation hydrodynamics calculations of
early dwarf galaxy formation. We develop a novel technique, adaptive ray
tracing, to accurately transport radiation from primordial stars. We find
primordial stellar feedback alters the landscape of early galaxy formation in
that its angular momentum is increased and baryon fractions are decreased. We
also describe the metal enrichment of the intergalactic medium and early dwarf
galaxies. Finally we explore cosmological reionization by these massive,
metal-free stars and its effects on star formation in early galaxies.
