  In the first part we calculate the boundary susceptibility $\chi_B$ in the
open $XXZ$-chain at zero temperature and arbitrary magnetic field $h$ by Bethe
ansatz. We present analytical results for the leading terms when $|h|\ll
\alpha$, where $\alpha$ is a known scale, and a numerical solution for the
entire range of fields. In the second part we calculate susceptibility profiles
near the boundary at finite temperature $T$ numerically by using the
density-matrix renormalization group for transfer matrices and analytically for
$T\ll 1$ by field theoretical methods. Finally we compare $\chi_B$ at finite
temperature with a low-temperature asymptotics which we obtain by combining our
Bethe ansatz result with recent predictions from bosonization.
