The Multiplex Fabry-Perot Interferometer (MFPI) is a unique instrument, incorporating the wide spectral-bandwidth capability of the Michelson interferometer with the small size and high resolution of the Fabry-Perot interferometer. The MFPI is, structurally, a standard Fabry-Perot in which the scanning distance is allowed to be very large, of the order of centimeters. The signal recorded through this distance is Fourier transformed as would be the interferogram produced by a Michelson interferometer. The result is a spectrum containing very high-resolution information over a moderately large optical bandwidth. The MFPI is much smaller than a Michelson producing the same resolution and covers a much broader bandwidth than a Fabry-Perot used in the usual fashion. We present a basic description of the operating theory for the MFPI in terms familiar to the Michelson spectroscopist.