  For a scattering system $\{A_\Theta,A_0\}$ consisting of selfadjoint
extensions $A_\Theta$ and $A_0$ of a symmetric operator $A$ with finite
deficiency indices, the scattering matrix $\{S_\gT(\gl)\}$ and a spectral shift
function $\xi_\Theta$ are calculated in terms of the Weyl function associated
with the boundary triplet for $A^*$ and a simple proof of the Krein-Birman
formula is given. The results are applied to singular Sturm-Liouville operators
with scalar and matrix potentials, to Dirac operators and to Schr\"odinger
operators with point interactions.
