  The High-Resolution Multi-Object Spectrograph (HRMOS) is a facility
instrument that we plan to propose for the Very Large Telescope (VLT) of the
European Southern Observatory (ESO), following the initial presentation at the
VLT 2030 workshop held at ESO in June 2019. HRMOS provides a combination of
capabilities that are essential to carry out breakthrough science across a
broad range of active research areas from stellar astrophysics and exoplanet
studies to Galactic and Local Group archaeology. HRMOS fills a gap in
capabilities amongst the landscape of future instrumentation planned for the
next decade. The key characteristics of HRMOS will be high spectral resolution
(R = 60000 - 80000) combined with multi-object (20-100) capabilities and long
term stability that will provide excellent radial velocity precision and
accuracy (10m/s). Initial designs predict that a SNR~100 will be achievable in
about one hour for a star with mag(AB) = 15, while with the same exposure time
a SNR~ 30 will be reached for a star with mag(AB) = 17. The combination of high
resolution and multiplexing with wavelength coverage extending to relatively
blue wavelengths (down to 380\,nm), makes HRMOS a spectrograph that will push
the boundaries of our knowledge and that is envisioned as a workhorse
instrument in the future.
  The science cases presented in this White Paper include topics and ideas
developed by the Core Science Team with the contributions from the astronomical
community, also through the wide participation in the first HRMOS Workshop
(https://indico.ict.inaf.it/event/1547/) that took place in Firenze (Italy) in
October 2021.
