  The intergalactic medium - the cosmic gas that fills the great spaces between
the galaxies - is affected by processes ranging from quantum fluctuations in
the very early universe to radiative emission from newly-formed stars. This
gives the intergalactic medium a dual role as a powerful probe both of
fundamental physics and of astrophysics. The heading of fundamental physics
includes conditions in the very early universe and basic cosmological
parameters. The astrophysics refers to chapters of the long cosmic history of
stars and galaxies that are being revealed through the effects of stellar
feedback on the cosmic gas. This review describes the physics of the
intergalactic medium, focusing on recent theoretical and observational
developments in understanding early cosmic history. In particular, radiation
from the earliest generation of stars is thought to have transformed the
universe, turning the surrounding atoms into free electrons and ions. Knowing
exactly when and how the reionization process happened is a primary goal of
cosmologists, because this would tell us when the early stars and black holes
formed and in what kinds of galaxies.
  Cosmic reionization is beginning to be understood with the help of
theoretical models and computer simulations. A wide variety of instruments
currently under design will probe the first sources of light during an epoch in
cosmic history that has been largely unexplored so far. The new observations
and the challenges for theoretical models and numerical simulations will
motivate intense work in this field over the coming decade. (abridged)

Astrophysics