  We propose a muon-proton collider with asymmetrical multi-TeV beam energies
and integrated luminosities of $0.1-1$ ab$^{-1}$. With its large center-of-mass
energies and yet small Standard Model background, such a machine can not only
improve electroweak precision measurements but also probe new physics beyond
the Standard Model to an unprecedented level. We study its potential in
measuring the Higgs properties, probing the R-parity-violating Supersymmetry,
as well as testing heavy new physics in the muon $g-2$ anomaly. We find that
for these physics cases the muon-proton collider can perform better than both
the ongoing and future high-energy collider experiments.
