The absorption lines found in the spectra of distant quasars provide a unique method of probing the physical conditions in the universe at early epochs. This thesis describes a study of the Lyman alpha forest absorption systems seen in the spectra of high redshift QSOs. The Anglo-Australian Telescope has been used to obtain high resolution spectra of several bright QSOs. Considerable effort has gone into developing statistical techniques for profile fitting to the data to objectively and reliably extract the parameters associated with each absorbing cloud. The distribution functions for these are given and discussed. Particular attention has been paid to the clustering properties of the Lyman alpha clouds and it is found that they are weakly (but significantly) clustered on small velocity scales. Possible interpretations of this result are discussed. One especially interesting aspect of QSO absorption systems concerns the potential for measuring, or obtaining limits on, the deuterium to hydrogen abundance at high redshifts. A knowledge of this quantity is important for constraining cosmological models and can also help us to understand the chemical evolution of light elements in galaxies. A series of numerical simulations has been carried out to explore the potential for such measurements and an absorption system has been analysed to obtain an upper limit to D/H at z = 3.