  We continue the study of boundary data maps, that is, generalizations of
spectral parameter dependent Dirichlet-to-Neumann maps for (three-coefficient)
Sturm-Liouville operators on the finite interval $(a,b)$, to more general
boundary conditions. While earlier studies of boundary data maps focused on the
case of general separated boundary conditions at $a$ and $b$, the present work
develops a unified treatment for all possible self-adjoint boundary conditions
(i.e., separated as well as non-separated ones).
  In the course of this paper we describe the connections with Krein's
resolvent formula for self-adjoint extensions of the underlying minimal
Sturm-Liouville operator (parametrized in terms of boundary conditions), with
some emphasis on the Krein extension, develop the basic trace formulas for
resolvent differences of self-adjoint extensions, especially, in terms of the
associated spectral shift functions, and describe the connections between
various parametrizations of all self-adjoint extensions, including the precise
relation to von Neumann's basic parametrization in terms of unitary maps
between deficiency subspaces.
