Quark masses from lattice QCD at the next-to-leading order

Using the results of several quenched lattice simulations, we predict the value of the strange and charm quark masses in the continuum at the next-to-leading order, m^{\overline{MS}}_s(\mu=2\,\, \rm{GeV})= (127 \pm 18)\,\, \rm{MeV} and m^{\overline{MS}}_{ch}(\mu=2 \,\,\rm{GeV})=(1.47 \pm 0.28)\,\, \rm{GeV}. The errors quoted above have been estimated by taking into account the original statistical error of the lattice results and the uncertainties coming from the matching of the lattice to the continuum theory. A detailed presentation of the relevant formulae at the next-to-leading order and a discussion of the main sources of errors is also presented.