Fourier transform spectroscopy is a technique that uses interference of light rather than dispersion to measure the spectrum of a substance. The basis of this technique is the Fourier-pair relationship between the interferogram (interference function) of a substance and its spectrum. This relationship and other important physical and mathematical principles of Fourier transform spectroscopy are reviewed, and the important role of mini-computers in the development and application of this technique is discussed. *Research sponsored by the Energy Research and Development Administration under contract with Union Carbide Corporation. tAlbert Abraham Michelson (1852-1931) was the first American to win a Nobel Prize in science. Hew was awarded the 1907 Prize in physics for spectroscopic and metrological studies carried out with his precision optical instruments. Sin order to measure the energy levels of a system, it is necessary to induce transitions between eigenstates. and this is accomplished by exposing a substance to electromagnetic radiation. Measuring the spectrum of a substance is a determination of its response to electromagnetic radiation QThe unit cm-' is the number of waves per cm. It has become the practice of many spectroscopists to refer to the energy of a transition expressed in cm-' as the frequency of the transition, whereas, strictly speaking, frequency is the number of oscillations per unit time, s-' (cycles per s).