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A short introduction into the theory of quantum gravitational systems with a finite number of degrees of freedom is given. The theory is based on the method of quantization of constrained systems. The state vector of the system satisfies a set of wave equations which describes the time evolution of the system in the space of quantum fields. The state vector in such an approach can be normalized to unity. The theory permits a generalization to negative values of the scale factor and, being applied to cosmology, leads to the new understanding of the evolution of the universe. It gives an insight into the reasons why the regime of the expansion may change from acceleration to deceleration or vice versa, revealing a new type of quantum forces acting like dark matter and dark energy in the universe.

Quantum Corrections to the Dynamics of the Gravitational System