  The paper develops a theory of spectral boundary value problems from the
perspective of general theory of linear operators in Hilbert spaces. An
abstract form of spectral boundary value problem with generalized boundary
conditions is suggested and results on its solvability complemented by
representations of weak and strong solutions are obtained. Existence of a
closed linear operator defined by a given boundary condition and description of
its domain are studied in detail. These questions are addressed on the basis of
Krein's resolvent formula derived from the explicit representations of
solutions also obtained here. Usual resolvent identities for two operators
associated with two different boundary conditions are written in terms of the
so called M-function. Abstract considerations are complemented by illustrative
examples taken from the theory of partial differential operators. Other
applications to boundary value problems of analysis and mathematical physics
are outlined. (Initial version title "Spectral Boundary Value Problems and
their Linear Operators", 2009)
