  The formation of the first galaxies is influenced by the radiative feedback
from the first generations of stars. This feedback is manisfested by the
heating and ionization of the gas which lies within the H II regions
surrounding the first stars, as well as by the photodissociation of hydrogen
molecules within the larger Lyman-Werner (LW) bubbles that surround these
sources. Using a ray-tracing method in three-dimensional cosmological
simulations, we self-consistently track the formation of, and radiative
feedback from, individual stars in the course of the formation of a
protogalaxy. We compute in detail the H II regions of each of these sources, as
well as the regions affected by their molecule-dissociating radiation. We
follow the thermal, chemical, and dynamical evolution of the primordial gas, as
it becomes incorporated into the protogalaxy. While the IGM is, in general,
optically thick to LW photons only over physical distances of > 30 kpc at
redshifts z < 20, the high molecule fraction that is built up in relic H II
regions and their increasing volume-filling fraction renders even the local IGM
optically thick to LW photons over physical distances of the order of a few
kiloparsecs. We find that efficient accretion onto Population III relic black
holes may occur after ~ 60 Myr from the time of their formation, by which time
the photo-heated relic H II region gas can cool and re-collapse into the 10^6
M_solar minihalo which hosts the black hole. Also, Pop II.5 stars, postulated
to have masses of the order of 10 M_solar, can likely form from this
re-collapsing relic H II region gas. Overall, we find that the local radiative
feedback from the first generations of stars suppresses the star formation rate
by only a factor of, at most, a few.
