  The top quark is the heaviest known elementary particle, with a mass about 40
times larger than the mass of its isospin partner, the bottom quark. It decays
almost 100% of the time to a $W$ boson and a bottom quark. Using top-antitop
pairs at the Tevatron proton-antiproton collider, the CDF and {\dzero}
collaborations have measured the top quark's mass in different final states for
integrated luminosities of up to 5.8 fb$^{-1}$. This paper reports on a
combination of these measurements that results in a more precise value of the
mass than any individual decay channel can provide. It describes the treatment
of the systematic uncertainties and their correlations. The mass value
determined is $173.18 \pm 0.56 \thinspace ({\rm stat}) \pm 0.75 \thinspace
({\rm syst})$ GeV or $173.18 \pm 0.94$ GeV, which has a precision of $\pm
0.54%$, making this the most precise determination of the top quark mass.
