A single crystal neutron spectrometer using a copper crystal has been designed and constructed for the purpose of studying the low energy (<1 ev) neutron spectrum from the V.P.I. reactor. The basic theory necessary for the design, the details of the spectrometer, calibration data and method of operation are presented in this thesis. A relation between angle of diffraction and neutron energy is obtained from the known lattice spacing of the copper crystal. A measure of the total cross section of cadmium from 0.01 to 1.0 ev has been obtained from transmission data for a thin cadmium sheet. The position of the low energy resonance peak confirms the computed calibration. The resolution of the instrument and the intensity of the diffracted beam as a function of energy were studied in order to ascertain the usable range of the spectrometer.