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Observations of high-redshift quasars show that the IGM must have beenreionized at some redshift $z>5$. If a source of radiation could be observed atthe rest-frame Lya wavelength, at a sufficiently high redshift where some ofthe IGM in the line-of-sight was not yet reionized, the Gunn-Peterson troughshould be present. Longward of the Lya wavelength, a damping wing should beobserved caused by the neutral IGM whose absorption profile can be predicted.Measuring the shape of this damping wing would provide irrefutable evidence ofthe observation of the IGM before reionization, and a determination of thedensity of the neutral IGM. This measurement might be hindered by the possiblepresence of a dense absorption system associated with the source.  Shortward of the \lya wavelength, absorption should be seen from the patchystructure of the IGM in the process of reionization. We show that a completeGunn-Peterson trough is most likely to continue to be observed through theepoch where the IGM is partially ionized. The damping wings of the neutralpatches should overlap if the proper pathlength through an ionized region isless than 1 h^{-1} Mpc; even in larger ionized regions, the characteristicbackground intensity should be low enough to yield a very high optical depthdue to the residual neutral fraction, although occasionally some flux may betransmitted through large, underdense voids within an ionized region. The caseof the HeII reionization is also discussed, and we argue that helium wasalready doubly ionized by z=3 throughout the IGM.  The recently discovered afterglows of gamma-ray bursts might soon be observedat very high redshifts. Their featureless continuum spectrum and highluminosities make them ideal sources for studying absorption by the IGM.Comment: submitted to Ap

Reionization of the Intergalactic Medium and the Damping Wing of the Gunn‐Peterson Trough