  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.
