B physics on the Lattice: $\overline{\Lambda}$, $\lambda_{1}$, $\overline{m}_{b}(\overline{m}_{b})$, $\lambda_2$, $B^{0}-\overline{B}^{0}$ mixing, $f_{B}$ and all that

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 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 estimates by combining results from three independent lattice simulations at