  We study the process of cosmic reionization and estimate the ionizing
background in the IGM using the Lyman series absorption in the spectra of the
four quasars at 5.7<z<6.3 discovered by the SDSS. We derive the evolution of
the ionizing background at high redshifts, using both semi-analytic techniques
and cosmological simulations to model the density fluctuations in the IGM. The
existence of the complete Ly alpha Gunn-Peterson trough in the spectrum of the
z=6.28 quasar SDSS 1030+0524 indicates a photoionization rate Gamma_{-12} at
z~6 lower than 0.08, at least a factor of 6 smaller than the value at z~3. The
Ly beta and Ly gamma Gunn-Peterson troughs give an even stronger limit
Gamma_{-12}<0.02 due to their smaller oscillator strengths, indicating that the
ionizing background in the IGM at z~6 is more than 20 times lower than that at
z~3. Meanwhile, the volume-averaged neutral hydrogen fraction increases from
10^{-5} at z~3 to >10^{-3} at z~6. At this redshift, the mass-averaged neutral
hydrogen fraction is larger than 1%; the mildly overdense regions (delta > 3)
are still mostly neutral and the comoving mean free path of ionizing photons is
shorter than 8 Mpc. Comparison with simulations of cosmological reionization
shows that the observed properties of the IGM at z~6 are typical of those in
the era at the end of the overlap stage of reionization when the individual HII
regions merge. Thus, z~6 marks the end of the reionization epoch. The redshift
of reionization constrains the small scale power of the mass density
fluctuations and the star forming efficiency of the first generation of
objects.
