Surprisingly, only a minority of the normal matter can be probed by observations of starlight from galaxies. This project aims, through an international collaboration, at studying the remaining 90% of the baryons traced by the intergalactic gas. Using a number of major Hubble Space Telescopes PI-programs in combination with both multi-wavelength datasets and state-of-the-art hydrodynamical simulations, the overarching objective is to study the physical processes by which gas travels into, through, and out of galaxies. These processes, which mostly take place in the immediate surrounding of galaxy (the so-called circum-galactic medium), may collectively be described as the cosmic baryon cycle. Such studies are essential to understand the formation of galaxies and the growth of structure in the Universe and hence impact the fields of astrophysics and cosmology.