An (e,2e) electron scattering spectrometer has been constructed and used for the first time to investigate the spectral momentum density of the valence bands of a solid target. This technique provides fundamental information about the electronic structure of both crystalline and amorphous solids. The three fundamental quantities, the band structure, electron density of states, and electron momentum distribution can be simultaneously derived from the measured (e,2e) cross section. A review of single electron and (e,2e) scattering theory is given with an emphasis on scattering from solids. The effects of multiple scattering are discussed and a method of deconvoluting those effects from the measured (e,2e) cross section is developed. There is a detailed description of the spectrometer design and operation with particular attention given to the electron optics and voltage distribution. The algorithms and software for computer aided data acquisition and analysis are also outlined, as is error analysis. The techniques employed in the preparation and characterization of extremely thin film samples of a-C and single crystal graphite are described. An analysis of the data taken for a-C samples is given. The data are compared with the results of complementary experiments and theory for graphite, diamond, and a-C which are given in a review of the literature. The existence of a definite dispersion relation ε(q) in amorphous carbon is demonstrated. The a-C band structure appears to be more similar to that of graphite than to that of diamond, however it differs significantly from both in some respects. The measured spectral momentum density seems compatible with a model of a-C based on small, randomly-oriented islands of quasi-2D graphite-like continuous random network structures. However, no definitive interpretations can be made until higher resolution experiments are performed on both a-C and single crystal graphite.Ph. D.