  In this paper Quantum Mechanics with Fundamental Length is chosen as the
theory for describing the early Universe. This is possible due to the presence
in the theory of General Uncertainty Relations from which unavoidable it
follows that in nature a fundamental length exits. Here Quantum
  Mechanics with Fundamental Length is obtained as a deformation of Quantum
Mechanics. The distinguishing feature of the proposed in this paper approach in
comparison with previous ones, lies on the fact that here density matrix
subjects to deformation as well as so far commutators had been deformed. The
deformed density matrix mentioned above, is named throughout this paper density
pro-matrix. Within our approach two main features of Quantum Mechanics are
conserved: the probabilistic interpretation of the theory and exact predefined
measuring procedure corresponding to that interpretation. The proposed here
approach allows to describe dynamics. In particular, the explicit form of
deformed Liouville's equation and the deformed Shr\"odinger's picture are
given. Some implications of obtained results are discussed. In particular, the
problem of singularity, the hypothesis of cosmic censorship, a possible
improvement of the statistical entropy definition and the problem of
information loss in black holes are considered.
