  We outline the unique role of a muon collider as a Higgs factory for Higgs
boson resonance production in the $s$-channel. Physics examples include: the
precision measurements of the Higgs mass and total width, and the resulting
ability to discriminate between the SM-like Higgs bosons of different models
such as between a light SM Higgs boson and the light Higgs boson of the MSSM;
the determination of the spin and coupling via the $h\to \tautau$ decay mode;
differentiation of two nearly degenerate heavy Higgs bosons by an energy scan;
and the ability to explore a general extended Higgs sector, possibly with
CP-violating couplings. The muon collider Higgs factory could perform
measurements that would be highly complementary to Higgs studies at the LHC and
LC; it would be likely to play a very crucial role in fully understanding the
Higgs sector.
