This thesis is a detailed presentation of a precision measurement of the mass of the $W$ boson. It has been obtained by analyzing $W o e u$ decays. The data used for this analysis was collected from 2002 to 2006 with the dzero~detector, during Run IIa of the Fermilab Tevatron collider. It corresponds to a total integrated luminosity of 1 fb$^{-1}$. With a sample of 499,830 $W o e u$ candidate events, we obtain a mass measurement of $M_W$=80.401 $pm$ 0.043 GeV. This is the most precise measurement from a single experiment to date.