  We lay out a comprehensive physics case for a future high-energy muon
collider, exploring a range of collision energies (from 1 to 100 TeV) and
luminosities. We highlight the advantages of such a collider over proposed
alternatives. We show how one can leverage both the point-like nature of the
muons themselves as well as the cloud of electroweak radiation that surrounds
the beam to blur the dichotomy between energy and precision in the search for
new physics. The physics case is buttressed by a range of studies with
applications to electroweak symmetry breaking, dark matter, and the naturalness
of the weak scale. Furthermore, we make sharp connections with complementary
experiments that are probing new physics effects using electric dipole moments,
flavor violation, and gravitational waves. An extensive appendix provides cross
section predictions as a function of the center-of-mass energy for many
canonical simplified models.
