The molecular gas phase is the material in galaxies out of which stars form. As such, it is this quantity that controls the star formation rate of a galaxy, thereby the overall stellar mass build-up, and ultimately galaxy evolution through cosmic time. In contrast to the decades-long studies of the stellar mass and star formation, characterising this fuel supply (ie molecular gas) in galaxies as a function of cosmic epoch has been in its infancy at the beginning of the project. The ALMA facility however redefined our ability to map out the cosmic cold gas supply, which triggered the ideas underlying this ERC program, through extensive observational ALMA programs led by the PI. In particular ASPECS was the first-ever approved ALMA large (150h) program of a cosmological deep field, aimed at providing a comprehensive view of the baryon cycle from gas to stars over cosmic time. ASPECS provided 3D molecular scans in two ALMA bands of the Hubble Ultra Deep Field (HUDF) -- the iconic cosmological deep field. Through this ERC, the molecular gas content of galaxies could thus be traced through cosmic history by targeting the iconic HUDF with ALMA. As vast multi-wavelength data for this field was available by previous international efforts, the molecular gas measurements could be immediately put in context with e.g. the stellar properties and star formation activity of the galaxies in the field. With these measurements, the project could thus constrain the cosmic baryon cycle, and quantify the gas flows within galaxies for the first time, providing a major breakthrough in the field. A second focus has been the detailed characterisation of the gas content in the host galaxies of the most distant quasars, when the Universe was less than one billion year old (<1/14th of today's age). These studies assess the role of cold gas in the build-up of the first massive cosmic structures in the Universe. This was achieved through a two-step process: first, a survey of dozens of quasar hosts with ALMA: this survey demonstrated the ubiquitousness of gas and dust already in the first Gyr of the universe, and showed that many of the targets lend themselves for high spatial resolution imaging. Indeed, follow-up observations on spatial scales of only a few hundred parsecs (typically only achieved in the local universe) constrained the kinematics of the quasar hosts, as well as their morphologies. One of the big surprises of these studies has been that the quasar host galaxies do not look like merging systems ("train wrecks"), but in many cases like simple rotating disks. This was unexpected, as these galaxies harbour accreting supermassive black holes with masses beyond one billion solar masses. However, their host galaxies appear to be unaffected by these central engines. In summary, the project capitalised on the unparalleled capabilities of ALMA and other facilities to map out the cosmic gas supply through cosmic history, from the first Gyr (cosmic dawn) to the peak of cosmic star formation (cosmic noon) to today's universe.
