  We derive the quantum Boltzmann equation for the two-dimensional electron gas
in a magnetic field such that the filling factor $\nu \gg 1$. This equation
describes all of the effects of the external fields on the impurity collision
integral including Shubnikov-de Haas oscillations, smooth part of the
magnetoresistance, and non-linear transport. Furthemore, we obtain quantitative
results for the effect of the external microwave radiation on the linear and
non-linear $dc$ transport in the system. Our findings are relevant for the
description of the oscillating resistivity discovered by Zudov {\em et al.},
zero-resistance state discovered by Mani {\em et al.} and Zudov {\em et al.},
and for the microscopic justification of the model of Andreev {\em et al.}. We
also present semiclassical picture for the qualitative consideration of the
effects of the applied field on the collision integral.
