We propose an instrument by applying the aperture synthesis technique to the Martin & Puplett type Fourier Transform Spectrometer in millimeter and sub-millimeter waves. We call this equipment Multi-Fourier Transform interferometer(MuFT). MuFT realizes a wide band imaging, spectroscopy and polarimetry in millimeter and sub-millimeter waves. The direct detectors, eg. bolometer, SIS video detector, can be used as the focal plane detectors. These type of detectors have a great advantage in FIR band since they are free from the quantum limit of the noise which limits the sensitivity of the heterodyne detectors used in the usual interferometers. Further, the direct detectors are able to make a large format array contrary to the usual interferometers in which usage of array detector is practically difficult. Above three characteristics make one be possible to develop high sensitive super broad band FIR interferometer with wide field of view. Fundamentals of the MuFT with results of laboratory experiments and current status of astronomical observations with MuFT are summarized. We did test observation with this system in the winter 2005. We also report concerning the observational result in 2006.