Search for the lepton-family-number nonconserving decay ${\mu }^{+}\to e^{+}\gamma$

The MEGA experiment, which searched for the muon- and electron-number violating decay ${\mu }^{+}\to e^{+}\gamma ,$ is described. The spectrometer system, the calibrations, the data taking procedures, the data analysis, and the sensitivity of the experiment are discussed. The most stringent upper limit on the branching ratio, $\mathcal{B}({\mu }^{+}\to e^{+}\gamma )<\mathrm{}1.2\mathrm{}\times {10}^{-11}$ with $90\%$ confidence, is derived from a likelihood analysis.