Higher Precision Measurement of the hfs Interval of Muonium and of the Muon Magnetic Moment

New higher precision measurements of the hyperfine Zeeman transitions in the ground state of muonium have been performed with use of the high-stopping-density surface ${\ensuremath{\mu}}^{+}$ beam at the Clinton P. Anderson Meson Physics Facility. The results are $\ensuremath{\Delta}\ensuremath{\nu}=4463\ensuremath{-}302.88(16)$ kHz (0.036 ppm) and $\frac{{\ensuremath{\mu}}_{\ensuremath{\mu}}}{{\ensuremath{\mu}}_{p}}=3.1833461(11)$ (0.36 ppm). The current theoretical value of $\ensuremath{\Delta}\ensuremath{\nu}$ agrees well with experiment within the 0.77-ppm error of $\ensuremath{\Delta}{\ensuremath{\nu}}_{\mathrm{theor}}$, which is due principally to inaccuracy in evaluation of the nonrecoil radiative correction term. The most precise current value of $\frac{{m}_{\ensuremath{\mu}}}{{m}_{e}}$ is obtained from our value of $\frac{{\ensuremath{\mu}}_{\ensuremath{\mu}}}{{\ensuremath{\mu}}_{p}}$.