Anisotropy of the Upper Critical Field and Critical Current in Single Crystal MgB$_2$

We report on specific heat, high magnetic field transport and $ac-$susceptibility measurements on magnesium diboride single crystals. The upper critical field $H_{c2}$ for magnetic fields perpendicular and parallel to the Mg and B planes is presented for the first time in the entire temperature range. A very different temperature dependence has been observed in the two directions which yields to a temperature dependent anisotropy with $\Gamma \sim$ 5 at low temperatures and about 2 near $T_c$. A peak effect is observed in susceptibility measurements for $H \sim $2 T parallel to the $c-$axis and the critical current density presnts a sharp maximum for $H$ parallel to the ab-plane.