These notes will be useful and of interest to mathematicians and
physicists active in research as well as for students with some
knowledge of the abstract theory of operators in Hilbert spaces. They
give a complete spectral theory for ordinary differential expressions of
arbitrary order n operating on -valued functions existence and
construction of self-adjoint realizations via boundary conditions,
determination and study of general properties of the resolvent, spectral
representation and spectral resolution. Special attention is paid to the
question of separated boundary conditions, spectral multiplicity and
absolutely continuous spectrum. For the case nm=2 (Sturm-Liouville
operators and Dirac systems) the classical theory of Weyl-Titchmarch is
included. Oscillation theory for Sturm-Liouville operators and Dirac
systems is developed and applied to the study of the essential and
absolutely continuous spectrum. The results are illustrated by the
explicit solution of a number of particular problems including the
spectral theory one partical Schrödinger and Dirac operators with
spherically symmetric potentials. The methods of proof are functionally
analytic wherever possible.