  The mass of the top quark is a fundamental parameter of the standard model
(SM) and has to be determined experimentally. In this talk, I present the most
recent measurements of the top quark mass in $p\bar p$ collisions at $\sqrt
s=1.96$~TeV recorded by the D0 experiment at the Fermilab Tevatron Collider.
The measurements are performed in final states containing two leptons, using
5.4~\fb of integrated luminosity, and one lepton, using 9.7~\fb of integrated
luminosity. The latter constitutes the most precise single measurement of the
mass of the top quark, corresponding to a relative precision of 0.43\%. I
conclude with a combination of our results with the results by the CDF
collaboration, attaining a relative precision of 0.37\%
