  In this report we discuss the main theories to understand the origin of
baryon and lepton number violation in physics beyond the Standard Model. We
present the theoretical predictions for rare processes such as neutrinoless
double beta decay, proton decay, and neutron-antineutron oscillation, and
overview the prospects to discover these rare processes in the near future. The
possibility to observe baryon and lepton violating signatures at current and
future colliders and through precision studies of other rare processes, and the
testability of different baryogenesis mechanisms is discussed in detail. A
healthy and broad experimental program looking for proton decay, neutrinoless
double beta decay and neutron-antineutron oscillations is essential to make new
discoveries in this field. These searches are carried out at various
experimental facilities in the US and abroad, and use instrumentation arching
across traditional HEP/NP boundaries. In addition, experiments such as those at
the Large Hadron Collider could discover exotic baryon and/or lepton number
violating signatures connected to low energy scale theories for neutrino
masses, supersymmetric models with R-parity violation, new gauge theories or
other mechanisms for physics beyond the Standard Model. The landscape presented
in this report could be crucial to discover the underlying mechanism for
neutrino masses and the matter-antimatter asymmetry in the universe.
