  Observations of high-redshift quasars show that the IGM must have been
reionized at some redshift $z>5$. If a source of radiation could be observed at
the rest-frame Lya wavelength, at a sufficiently high redshift where some of
the IGM in the line-of-sight was not yet reionized, the Gunn-Peterson trough
should be present. Longward of the Lya wavelength, a damping wing should be
observed caused by the neutral IGM whose absorption profile can be predicted.
Measuring the shape of this damping wing would provide irrefutable evidence of
the observation of the IGM before reionization, and a determination of the
density of the neutral IGM. This measurement might be hindered by the possible
presence of a dense absorption system associated with the source.
  Shortward of the \lya wavelength, absorption should be seen from the patchy
structure of the IGM in the process of reionization. We show that a complete
Gunn-Peterson trough is most likely to continue to be observed through the
epoch where the IGM is partially ionized. The damping wings of the neutral
patches should overlap if the proper pathlength through an ionized region is
less than 1 h^{-1} Mpc; even in larger ionized regions, the characteristic
background intensity should be low enough to yield a very high optical depth
due to the residual neutral fraction, although occasionally some flux may be
transmitted through large, underdense voids within an ionized region. The case
of the HeII reionization is also discussed, and we argue that helium was
already doubly ionized by z=3 throughout the IGM.
  The recently discovered afterglows of gamma-ray bursts might soon be observed
at very high redshifts. Their featureless continuum spectrum and high
luminosities make them ideal sources for studying absorption by the IGM.
