A precision luminosity measurement in the ZEUS experiment at the HERA electron--proton collider is described, based on the data collected by the ZEUS luminosity monitor in 1996. The method of the measurement relies on the detection of high-energy photons from the ep bremsstrahlung process. The large cross section of this process allows for the continuous and fast monitoring of the HERA luminosity as well as for the control of the electron beam steering and focusing. A 1% precision of the luminosity determination has been achieved. The luminosity monitor has been also extensively used for studying quasi-real photoproduction, and radiative processes in deep inelastic scattering.

PACS numbers: 06.60.Mr