**Abstract: ** In many geometric situations, separation of variables renders a Dirac
operator as a generalized ordinary differential equation, with some
specific properties, though. In joint work with Werner Ballmann and
Gilles Carron I have abstracted from this fact the notion of Dirac
system which will be discussed in this lecture. Being essentially a one
dimensional notion, no specific knowledge of the geometry and not even
the specific definition of the Dirac operator is necessary to understand
the vital properties of such systems. We will apply the theory to be
developed to spectral properties of Dirac operators near infinity, in
particular to the determination of the essential spectrum.