Quantum geometrodynamics of the Blanchi-IX model in extended phase space

A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noni nvariant and thus consistent with the observation conditions of a closed un iverse, by that being considerably distinguished from the traditional Wheel er-DeWitt one. For the Bianchi-M cosmological model it is shown that a norm alizable wave function of the universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Sc hrodinger equation. The Wheeler-DeWitt quantum geometrodynamics is represen ted a singular, BRST-invariant solution to the Schrodinger equation having no property of normalizability.