We present a resonant cavity approach for non-invasive, pulse-to-pulse, beam emittance measurements of non-circular multi-bunch beams. In a resonant cavity, desired field components can be enhanced up to Q{sub L{lambda}}/{pi}, where Q{sub L{lambda}} is the loaded quality factor of the resonant mode {lambda}, when the cavity resonant mode matches the bunch frequency of a bunch-train beam pulse. In particular, a quad-cavity, with its quadrupole mode (TM{sub 220} for rectangular cavities) at beam operating frequency, rotated 45{sup o} with respect to the beamline, extracts the beam quadrupole moment exclusively, utilizing the symmetry of the cavity and some simple networks to suppress common modes. Six successive beam quadrupole moment measurements, performed at different betatron phases in a linear transport system determine the beam emittance, i.e. the beam size and shape in the beam's phase space, if the beam current and position at these points are known. In the presence of x-y beam coupling, ten measurements are required. One measurement alone provides the rms-beam size of a large aspect ratio beam. The resolution for such a measurement of rms-beam size with the rectangular quad-cavity monitor presented in this article is estimated to be on the order of ten microns. A prototype quad-cavity was fabricated and preliminary beam tests were performed at the Next Linear Collider Test Accelerator (NLCTA) at the Stanford Linear Accelerator Center (SLAC). Results were mainly limited by beam jitter and uncertainty in the beam position measurement at the cavity location. This motivated the development of a position-emittance integrated monitor
