  The Hall conductance of a two-dimensional electron gas has been studied in a
uniform magnetic field. The Hall conductivity is expressed as a sum of two
contributions: one corresponding to the classical Drude-Zener formula, and a
second which has no classical analogy. The developed theory is applied to the
Hall effect. The Kobo formula is written in a form that makes apparent the
quantization when the Fermi energy lies in a gap. We examine the hierarchical
spectral flow of Hall conductivity.
