  We present topological features of the magnetic response (orbital and spin)
of a two-dimensional degenerate and non interacting electron gas due to
inhomogeneous applied magnetic fields. These issues are analysed from the point
of view of the Index theory with a special emphasis on the non perturbative
aspects of this response. The limiting case of a Aharonov-Bohm magnetic flux
line is studied in details and the results are extended to more general
situations.
