  We discuss the renormalization of different definitions of quark masses in
the Wilson and the tree-level improved SW-Clover fermionic action. For the
improved case we give the correct relationship between the quark mass and the
hopping parameter. Using perturbative and non-perturbative renormalization
constants, we extract quark masses in the $\MSbar$ scheme from Lattice QCD in
the quenched approximation at $\beta=6.0$, $\beta=6.2$ and $\beta=6.4$ for both
actions. We find: $\bar{m}^{\MSbar}(2 GeV)=5.7 \pm 0.1 \pm 0.8$ MeV,
$m_s^{\MSbar}(2GeV)= 130 \pm 2 \pm 18 $ MeV and $m_c^{\MSbar}(2 GeV) = 1662\pm
30\pm 230$ MeV.
