This thesis describes a first measurement of the W Boson mass through the decay into a muon and a neutrino in Run 2 of the Tevatron. The W Bosons are produced in proton-antiproton collisions at a center of mass energy of 1.96 TeV. The data sample used for this analysis corresponds to 200 pb{sup -1} recorded by the upgraded Collider Detector at Fermilab. The most important quantity in this measurement is the momentum of the muon measured in a magnetic spectrometer which is calibrated using the two quarkonium resonances J/{Psi} and {Upsilon}(1S). Systematic uncertainties arise from the modeling of the recoil when the W Boson is produced, the momentum calibration, the modeling of W Boson production and decay dynamics and backgrounds. The result is: M{sub W} = 80408 {+-} 50(stat.) {+-} 57(syst.) MeV/c{sup 2}
