  We define and study the properties of Darboux-type transformations between
Sturm--Liouville problems with boundary conditions containing rational
Herglotz--Nevanlinna functions of the eigenvalue parameter (including the
Dirichlet boundary conditions). Using these transformations, we obtain various
direct and inverse spectral results for these problems in a unified manner,
such as asymptotics of eigenvalues and norming constants, oscillation of
eigenfunctions, regularized trace formulas, and inverse uniqueness and
existence theorems.
