  The occurrence of the neutrinoless decay 0n-bb mode has fundamental
consequences: first total lepton number is not conserved, and second, the
neutrino is a Majorana particle. Further the effective mass measured allows to
put an absolute scale of the neutrino mass spectrum. In addition, double beta
experiments yield sharp restrictions also for other beyond standard model
physics. These include SUSY models, leptoquarks (leptoquark-Higgs
coupling),compositeness, left-right symmetric models (right-handed W boson
mass), test of special relativity and of the equivalence principle in the
neutrino sector and others. First evidence for neutrinoless double beta decay
was given in 2001, by the HEIDELBERG-MOSCOW experiment. The HEIDELBERG-MOSCOW
experiment is the by far most sensitive 0-nu-bb experiment since more than 10
years. It operated 11 kg of enriched 76Ge in the Gran Sasso. The collected
statistics in the period 1990 - 2003 is 71.7 kgy. The background achieved in
the energy region of the Q value for double beta decay is 0.11events/kgykeV.
The two-neutrino accompanied half-life is determined on the basis of more than
100000 events to be (1.74. {+0.18}{-0.16})x10^{21}years. The confidence level
for the neutrinoless signal is 4.2 sigma level (more than 5 sigma in the
pulse-shape-selected spectrum). The half-life is T_{1/2}^{0\nu}=(1.19{+0.37}
{-0.23})x10^{25}years. The effective neutrino mass deduced is (0.2-0.6)eV
(99.73% c.l.), i.e. neutrinos have degenerate masses, and consequently can
considerably contribute to hot dark matter in the Universe. The sharp
boundaries for other beyond SM physics, mentioned above, are comfortably
competitive to corresponding results from high-energy accelerators like
TEVATRON, HERA, etc. Some discussion is given on future beta-beta experiments.
