  The first dwarf galaxies, which constitute the building blocks of the
collapsed objects we find today in the Universe, had formed hundreds of
millions of years after the big bang. This pedagogical review describes the
early growth of their small-amplitude seed fluctuations from the epoch of
inflation through dark matter decoupling and matter-radiation equality, to the
final collapse and fragmentation of the dark matter on all mass scales above
\~10^{-4} solar masses. The condensation of baryons into halos in the mass
range of ~10^5-10^{10} solar masses led to the formation of the first stars and
the re-ionization of the cold hydrogen gas, left over from the big bang. The
production of heavy elements by the first stars started the metal enrichment
process that eventually led to the formation of rocky planets and life. A wide
variety of instruments currently under design [including large-aperture
infrared telescopes on the ground or in space (JWST), and low-frequency arrays
for the detection of redshifted 21cm radiation], will establish better
understanding of the first sources of light during an epoch in cosmic history
that was largely unexplored so far. Numerical simulations of reionization are
computationally challenging, as they require radiative transfer across large
cosmological volumes as well as sufficently high resolution to identify the
sources of the ionizing radiation. The technological challenges for
observations and the computational challenges for numerical simulations, will
motivate intense work in this field over the coming decade.
