  A theory of integer quantum Hall effect(QHE) in realistic systems based on
von Neumann lattice is presented. We show that the momentum representation is
quite useful and that the quantum Hall regime(QHR), which is defined by the
propagator in the momentum representation, is realized. In QHR, the Hall
conductance is given by a topological invariant of the momentum space and is
quantized exactly. The edge states do not modify the value and topological
property of $\sigma_{xy}$ in QHR. We next compute distribution of current based
on effective action and find a finite amount of current in the bulk and the
edge, generally. Due to the Hall electric field in the bulk, breakdown of the
QHE occurs. The critical electric field of the breakdown is proportional to
$B^{3/2}$ and the proportional constant has no dependence on Landau levels in
our theory, in agreement with the recent experiments.
