Nuclear double beta decay is one of the most promising tools for probing beyond-the-standard-model physics on beyond-accelerator energy scales. It is already now probing the TeV scale, on which new physics should manifest itself according to theoretical expectations. Only in the early 1980s was it known that double beta decay yields information on the Majorana mass of the exchanged neutrino. At present, the sharpest bound for the electron neutrino mass arises from this process. It is only in the last 10 years that the much more far-reaching potential of double beta decay has been discovered. Today, the potential of double beta decay includes a broad range of topics that are equally relevant to particle physics and astrophysics, such as masses of heavy neutrinos, of sneutrinos, as SUSY models, compositeness, leptoquarks, left-right symmetric models, and tests of Lorentz symmetry and equivalence principle in the neutrino sector. Double beta decay has become indispensable nowadays for solving the problem of the neutrino mass spectrum and the structure of the neutrino mass matrix — together with present and future solar and atmospheric neutrino oscillation experiments. Some future double beta experiments (like GENIUS) will be capable to be simultaneously neutrino observatories for double beta decay and low-energy solar neutrinos, and observatories for cold dark matter of ultimate sensitivity.This invaluable book outlines the development of double beta research from its beginnings until its most recent achievements, and also presents the outlook for its highly exciting future.