The Evolution of the Lyman Alpha Forest From Redshift 3 to 0

I review results obtained from studies of the high-redshift Lyman alpha forest, and present new results from HST/STIS spectra of low-redshift quasars in comparison with cosmological hydrodynamic simulations. The evolution of the Lyman alpha forest from redshift 3 to 0 is well-described by current structure formation models, in which Ly-a forest absorbing gas at all redshifts traces moderate-overdensity large-scale structures. I describe some of the insights provided by hydrodynamic simulations into the observed statistical trends of Ly-a absorbers and the physical state of the absorbing gas.