The Lyman-alpha forest refers to numerous, narrow neutral hydrogen absorption
lines blueward of the Lyman-alpha emission line ofhigh-redshift QSOs.
The current paradigm of the Lyman-alpha forest favors that it arises from moderate
amplitude density fluctuations in the warm (~10^4 K) photoionized, diffuse intergalactic medium(IGM) which traces the dark matter distribution in a simple manner. This interpretation has turned the Lyman-alpha forest into powerful cosmological probe at high redshifts, such as the matter power spectrum at smallest scales.
They also provide a constraint onthe feedback between high-redshift galaxies
and the IGM. At lower redshifts, the absorptions seen in low-redshift QSOs provide a
clue on the missing baryon. In addition to this general discussion on the importance
of the IGM, I will briefly discuss the current and upcoming instruments to study the IGM, such as COS on HST and the CODEX on the E-ELT.