  We introduce the scientific motivations for the development of the Cassegrain
U-Band Efficient Spectrograph (CUBES) that is now in construction for the Very
Large Telescope. The assembled cases span a broad range of contemporary topics
across Solar System, Galactic and extragalactic astronomy, where observations
are limited by the performance of current ground-based spectrographs shortwards
of 400nm. A brief background to each case is presented and specific technical
requirements on the instrument design that flow-down from each case are
identified. These were used as inputs to the CUBES design, that will provide a
factor of ten gain in efficiency for astronomical spectroscopy over 300-405nm,
at resolving powers of R~24,000 and ~7,000. We include performance estimates
that demonstrate the ability of CUBES to observe sources that are up to three
magnitudes fainter than currently possible at ground-ultraviolet wavelengths,
and we place its predicted performance in the context of existing facillities.
