  We present a short review of our most recent high statistics lattice
determinations in the HQET of the following important parameters in B physics:
the B--meson binding energy, $\overline{\Lambda}$ and the kinetic energy of the
b quark in the B meson, $\lambda_1$, which due to the presence of power
divergences require a non--perturbative renormalization to be defined; the
$\overline{MS}$ running mass of the b quark,
$\overline{m}_{b}(\overline{m}_{b})$; the $B^{*}$--$B$ mass splitting, whose
value in the HQET is determined by the matrix element of the chromo--magnetic
operator between B meson states, $\lambda_2$; the B parameter of the
$B^{0}$--$\bar{B}^{0}$ mixing, $B_{B}$, and the decay constant of the B meson,
$f_{B}$. All these quantities have been computed using a sample of $600$ gauge
field configurations on a $24^{3}\times 40$ lattice at $\beta=6.0$. For
$\overline{\Lambda}$ and $\overline{m}_{b}(\overline{m}_{b})$, we obtain our
estimates by combining results from three independent lattice simulations at
$\beta=6.0$, $6.2$ and $6.4$ on the same volume.
