  Total and differential cross sections for inclusive $J/\psi$ production have
been measured in $\sqrt{s} =$ 200 GeV proton-proton collisions at BNL-RHIC.
$J/\psi$ particles have been identified via $\mu^{+}\mu^{-}$ decays measured in
the forward muon spectrometer covering $1.2 < y < 2.2$ and via $e^{+}e^{-}$
decays measured in the mid-rapidity spectrometers of the PHENIX experiment.
Details of the muon channel measurement are presented in this paper based upon
an 81-nb$^{-1}$ integrated luminosity obtained in the first p+p run at RHIC.
Results are compared with previous experiments as well as theoretical model
predictions.
