  In April 2021, scientists active in muon physics met to discuss and work out
the physics case for the new High-Intensity Muon Beams (HIMB) project at PSI
that could deliver of order $10^{10}$\,s$^{-1}$ surface muons to experiments.
Ideas and concrete proposals were further substantiated over the following
months and assembled in the present document. The high intensities will allow
for completely new experiments with considerable discovery potential and unique
sensitivities. The physics case is outstanding and extremely rich, ranging from
fundamental particle physics via chemistry to condensed matter research and
applications in energy research and elemental analysis. In all these fields,
HIMB will ensure that the facilities S$\mu$S and CHRISP on PSI's High Intensity
Proton Accelerator complex HIPA remain world-leading, despite the competition
of muon facilities elsewhere.
