Nuclear structure and the double beta decay. Grand unification and supersymmetry

The mechanism of lepton number violation within the neutrinoless double beta decay (0νββ-decay) is discussed in context of the problem of neutrino mixing and the R-parity violating supersymmetric extensions of the Standard model. The problem of reliable determination of the nuclear matrix elements governing both two-neutrino and neutrinoless modes of the double beta decay is addressed. The limits on the lepton number violating parameters extracted from Heidelberg-Moscow 0νββ-decay experiment are listed. Studies in respect to future 0νββ-decay experimental projects are also presented. (author)