Gravitational lensing has tremendously contributed to our understanding of the mass distribution in galaxy clusters and of the distant Universe. Progress in this field has been extremely rapid, thanks to major advances in observation and theory. By exploiting superb HST imaging and extensive VLT spectroscopy, our group has played a key role. We have led observational and modeling programs resulting in 1) the best predictions of position, magnification and time delay of a lensed supernova, 2) the detection of an excess of small-scale gravitational lenses in observed galaxy clusters, and 3) the identification of hundreds of star-forming regions in lensed galaxies at redshift z~2-6. The time has thus come to plan the next-generation cluster mass models, taking advantage of the unique capabilities of the lensing softwares we have been using and of the multi-wavelength data already in hand (VLT/MUSE, HAWK-I, XShooter, FORS2; HST/UVIS; APEX/NFLASH; VISTA/VIRCAM; Chandra X-ray) and that we will receive shortly (JWST/NIRISS, NIRSpec, and NIRCam; Euclid).
After 90 years from its first estimate, the exact value of the cosmic expansion rate, the Hubble constant (H ), is still hotly debated. The current best measurements of H cannot be reconciled and this might point to exciting new physics. GRAAL proposes to use the time delays between the multiple images of supernovae and quasars, strongly lensed by galaxy clusters, to place crucial constraints on H and the parameters defining the global geometry of the Universe. This method is completely independent from and potentially competitive to the other cosmological probes. The timing is ideal to discover in forthcoming wide-field surveys (e.g. LSST) the first ~10 transient and variable sources lensed by clusters and to measure the most relevant cosmological quantities. The comparison of the unprecedented results of this study about the cluster dark matter distribution and amount of mass in sub-halos with the outcomes of the most advanced N-body and hydro simulations will enable novel tests of the assumed collisionless, cold nature of dark matter and of the role played by baryons in the process of structure formation. We will also investigate magnified galaxies and spatially resolve them down to few tens of pc. Such small scales can only be probed thanks to the exquisite resolution of current instrumentation (e.g. HST and VLT/MUSE, HAWK-I with adaptive optics) combined with lensing magnification. The smallest star-forming regions are likely individual, gravitationally bound, star clusters. Studying such complexes is key to understanding how star formation proceeds at high z, how galaxies build up their stellar mass, what are the sources that re-ionized the Universe, and how globular clusters formed. Hydro simulations of high-z galaxies hosting star clusters will support the interpretation of observations and set the stage for future ones with next-generation VLT instruments and the ELT.