Most matter in our Universe is not in the form of atoms and electrons: the ordinary matter of which we have direct experience; instead, it consists of "dark matter”, whose nature is still unknown. Our current dark matter theory explains well the formation of most galaxies in the Universe except for so-called ultra-diffuse galaxies that show an anomalous behaviour. In analogy to the anomaly in Mercury’s orbit that 100 years ago opened the path to Einstein’s General Relativity, this project will explore whether these galaxies may indicate a crack in our current theory and unveil the nature of dark matter.