  We consider the formulation and some elaboration of p-adic and adelic quantum
cosmology. The adelic generalization of the Hartle-Hawking proposal does not
work in models with matter fields. p-Adic and adelic minisuperspace quantum
cosmology is well defined as an ordinary application of p-adic and adelic
quantum mechanics. It is illustrated by a few minisuperspace cosmological
models in one, two and three minisuperspace dimensions. As a result of p-adic
quantum effects and the adelic approach, these models exhibit some discreteness
of the minisuperspace and cosmological constant. In particular, discreteness of
the de Sitter space and its cosmological constant is emphasized.
