Physics of Higgs Factories

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.