  Multidimensional cosmological models with $n~(n > 1)$ Einstein spaces are
discussed classically and with respect to canonical quantization. These models
are integrable in the case of Ricci flat internal spaces. For negative
curvature of the external space we find exact classical solutions modelling
dynamical as well as spontaneous compactification of the internal spaces.
Spontaneous compactification turns out to be an attractor solution. Solutions
of the quantum Wheeler-DeWitt equation are also obtained. Some of them describe
the tunneling process to be interpreted as the birth of the universe from
''nothing''.
