The talk is devoted to perturbation determinants for proper
self-adjoint and non-selfadjoint extensions of densely defined
closed symmetric operators to which the
classical definition of Gohberg and Krein does not apply
directly.
We approach to this problem in the framework of boundary
triplets for symmetric operators. Important will be the notion of
almost solvable extensions for which we prove some result of
independent interest. The result are used to deduce
trace formulas for pairs of extensions, in particular, for pairs of
accumulative, dissipative  and arbitrary extensions.
Finally, we give some applications to differential operators
with non-selfadjoint boundary conditions.
<BR> <BR>
The talk is based on a common work with Mark Malamud.

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<A HREF="Neidhardt.pdf">
Here you will find a formatted version of the abstract</A>.