  We generalize the notion of Lagrangian subspaces to self-orthogonal subspaces
with respect to a (skew-)symmetric form, thus characterizing
(skew-)self-adjoint and unitary operators by means of self-ortho-gonal
subspaces. By orthogonality preserving mappings, these characterizations can be
transferred to abstract boundary value spaces of (skew-)symmetric operators.
Introducing the notion of boundary systems we then present a unified treatment
of different versions of boundary triples and related concepts treated in the
literature. The application of the abstract results yields a description of all
(skew-)self-adjoint realizations of Laplace and first derivative operators on
graphs.
