Galaxies form and build up gradually, through discrete merger events and through the accretion of gas from the intergalactic medium. They also lose mass, driven out by internal causes such as galactic winds or by external effects such as tidal forces or ram pressure stripping. Understanding these processes as well as their interplay is key to understanding galaxy evolution. The principal battleground between inflows, outflows, and gas recycling is located well outside of the main stellar body of a galaxy (but still bound to its gravitational potential), now generally denoted as the "circumgalactic medium" (CGM). This project is advancing a new approach to investigate the structure and the dynamics of gas flows in the CGM, by employing the technique of integral field spectroscopy, or spectro-mapping, in various emission lines, using extensive observational data from the MUSE instrument at the Very Large Telescope (VLT) of the European Southern Observatory in Chile, and from the HETDEX survey conducted with the 10m Hobby-Eberly Telescope in Texas. The principal challenge for CGM studies is the extreme faintness of the its emission, which until now made spectro-mapping unfeasible except for a few extreme objects. Due to several technological and methodical advances we have finally achieved the sensitivity required to detect the CGM directly in emission through imaging spectroscopy, routinely for large representative samples of typical galaxies over a wide range of cosmic epochs. This will close important gaps in our understanding of galaxy formation and evolution, one of the most fundamental quests in modern astrophysical research. We aim at a thorough morphological and kinematical characterisation of the CGM, including constraints on its small-scale structure, to obtain a census over different galaxy types and at different cosmic times. One specific goal is the detection and dissection of the properties of circumgalactic outflows, believed to play a crucial role in the cosmic matter cycle in and around galaxies. Another particularly challenging objective is to directly trace the emission from inflowing intergalactic gas feeding the CGM and its central galaxy. Comparisons with other observational approaches as well as dedicated physical models and computer simulations are harnessed to interpret these various lines of evidence and form a more comprehensive picture of the processes and consitions in the circumgalactic medium.
