Abstract
High-resolution, high-S/N observations of the Lyman forest extend now from redshift zero to six, providing new insight into the physical conditions of the intergalactic medium and its evolution over more than 90% of the cosmic time. The universal expansion, the UV ionizing background and the gravitational condensation of structures are the driving factors shaping the number density and the column density distribution of the absorbers. A (limited) contribution of UV photons produced by galaxies is found to be important to reproduce the observed evolutionary pattern at very high and low redshift. The Lyman forest contains most of the baryons, at least at z > 1.5, and acts as a reservoir for galaxy formation. The typical Doppler parameter at a fixed column density is measured to slightly increase with decreasing redshift, but the inferred temperature at the mean density is increasing with redshift. The signatures of HeII reionization and feedback from the formation of galactic structures have possibly been detected in the Lyman forest.