  The Glauber approach to the gluon density in a nucleus, suggested by A.
Mueller, is developed and studied in detail. Using the GRV parameterization for
the gluon density in a nucleon, the value as well as energy and $Q^2$
dependence of the gluon density in a nucleus is calculated. It is shown that
the shadowing corrections are under theoretical control and are essential in
the region of small $x$. They change crucially the value of the gluon density
as well as the value of the anomalous dimension of the nuclear structure
function, unlike of the nucleon one. The systematic theoretical way to treat
the correction to the Glauber approach is developed and a new evolution
equation is derived and solved. It is shown that the solution of the new
evolution equation can provide a selfconsistent matching of ``soft" high energy
phenomenology with ``hard" QCD physics.
