  In a configuration space whose boundary can be identified with a subset of
its interior, a boundary condition can relate the behaviour of a function on
the boundary and in the interior. Additionally, boundary values can appear as
additive perturbations. Such boundary conditions have recently provided insight
into problems form quantum field theory. We discuss interior-boundary
conditions in an abstract setting, with a focus on self-adjoint operators,
proving self-adjointness criteria, resolvent formulas, and a classification
theorem.
