Martin Haehnelt MPA-Garching Cosmology with the Lyman alpha forest In the last few years a new paradigm for the origin of the Lyman alpha forest in the spectra of distant QSO's has been established by both new observations and numerical simulations. The Lyman alpha forest is now generally believed to arise from fluctuations in a warm (10^4 K) photoionized intergalactic medium which traces the large scale distribution of dark matter in a simple fashion. I discuss some of the exiting new possibilities to probe the distribution of dark matter, to constrain cosmological parameters and to investigate the thermal and metal enrichment history of the intergalactic medium.