This proposal aims to significantly enhance our knowledge of diffuse gas in the universe and its association with galaxies. Better understanding of the properties and physical state of the intergalactic medium (IGM) will not only shed light on processes related to galaxy formation and evolution, but will also provide a more complete census of baryons in the universe with implications for the missing baryons problem in cosmology. In addition, studying the interface between galaxies and the IGM, and the mechanisms for the dispersal of metal-rich gas and dust on large scales, may turn out to be crucial for high precision cosmology. One of the most useful ways to probe gaseous processes on both galactic and large IGM scales is through the study of quasar absorption line systems. Here I propose a combined theoretical and observational approach to investigate those systems, having in mind the new observational capabilities provided by large surveys and the recent revival of UV spectroscopy. More specifically, archival data will be used and augmented by follow-up observations (with HST and ground telescopes) to study physically motivated aspects of the IGM-galaxy interface. On the theoretical side, new computational means will provide ever more realistic predictions whose quality can be matched with that of upcoming observations. In particular, a new code will be devised on a new type of hardware, which will simulate the relevant gaseous processes, and whose predictions will be cast in a form suitable for comparison with absorption spectra. This will provide more quantitative tests for theoretical models that exploit the full potential of upcoming data products. This synergistic approach will shed light on long-standing questions pertaining to the physics of the IGM, the role of galaxy-IGM interaction in shaping galaxies, and may have far-reaching implications for cosmology and high-energy physics.