  The talk is devoted to the "extended phase space" approach to Quantum
Geometrodynamics. The premises that have led to the formulation of this
approach are briefly reviewed, namely, non-trivial topology of the Universe
which implies the absence of asymptotic states, in contrast to situations one
usually deals in ordinary quantum field theory; parametrization noninvariance
in the Wheeler - DeWitt theory; the problem of time and the absence of
dynamical evolution. Then we discuss the main features of the approach:
Hamiltonian dynamics in extended phase space, gauge-dependent Schrodinger
equation for the wave function of the Universe, the description of quantum
Universe from the viewpoint of observers in a wide enough class of reference
frames. After all, we analyse problems arising in this approach: the structure
of Hilbert space in Quantum Geometrodynamics, the relations between solutions
for the wave function of the Universe corresponding to various reference
frames, properties of a medium to be necessary to fix a reference frame, the
transition to classical limit.

General Relativity and Quantum Cosmology