The numerous absorption features observed in quasar spectra
blue-wards of their Lyman-alpha emission line (known as the Lyman-alpha
forest), provide one of the main probes of the IGM.  On scales smaller
than the Jeans scale the baryonic gas is smoothed by pressure forces
where the width of the absorption features is determined by the gas
thermodynamical properties. This smoothing facilitates the measurement
of the IGM temperature and temperature-density relation. On scales
larger than the Jeans scale, however, the gas distribution faithfully
follows that of the underlying dark matter. The gas distribution on
these scales provides a probe of the matter distribution and its power
spectrum. In this talk I'll show how these features have been utilised
to constrain the temperature evolution of the IGM and the Epoch of
Reionization as well as to measure the initial density fluctuations in
the Universe.