This grant covers experimental Elementary Particle Physics research by a group at Stanford University in collaboration with other NSF and DOE supported scientists. The group will search for very rare decays of the K-meson. Previous searches by this group have established the present world limits on nonconservation of lepton number. The new experiment should improve those limits by over a factor of ten. Within the Standard Model of quarks and leptons, such decays are forbidden. If observed, such decays would open a window on physics beyond the Standard Model.