Neutrino Mass from Laboratory: Contribution of Double Beta Decay to the Neutrino Mass Matrix

Double beta decay is indispensable to solve the question of the neutrino mass matrix together with $\nu$ oscillation experiments. The most sensitive experiment - since eight years the HEIDELBERG-MOSCOW experiment in Gran-Sasso - already now, with the experimental limit of $<m_\nu > < 0.26$ eV practically excludes degenerate $\nu$ mass scenarios allowing neutrinos as hot dark matter in the universe for the smallangle MSW solution of the solar neutrino problem. It probes cosmological models including hot dark matter already now on the level of future satellite experiments MAP and PLANCK. It further probes many topics of beyond SM physics at the TeV scale. Future experiments should give access to the multi-TeV range and complement on many ways the search for new physics at future colliders like LHC and NLC. For neutrino physics some of them (GENIUS) will allow to test almost all neutrino mass scenarios allowed by the present neutrino oscillation experiments.