  Standard techniques of canonical gravity quantization on the superspace of
3--metrics are known to cause insurmountable difficulties in the description of
time evolution. We forward a new quantization procedure on the superspace of
true dynamic variables -- geometrodynamic quantization. This procedure takes
into account the states that are ``off-shell'' with respect to the constraints
and thus circumvents the notorious problems of time. In this approach quantum
geometrodynamics, general covariance, and the interpretation of time emerge
together as parts of the solution to the total problem of geometrodynamic
evolution.
