Recent CMS results on Higgs boson physics

Two recent and prominent results in Higgs boson physics from the CMS experiment are presented. The major result is the first evidence for the Higgs boson decay to a pair of muons, and therefore for its coupling to second generation fermions, a milestone in establishing the Higgs boson properties. Also presented are new searches for the nonresonant production of Higgs boson pairs via gluon and weak boson fusion processes in final states with two bottom quarks and two photons, yielding most stringent constraints to date on these productions, and on the Higgs boson self-coupling.