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We present here the transcripts of lectures and talks which were delivered at the NATO ADVANCED STUDY INSTITUTE 'Electrons in Disordered Hetals and at ~~etallic Surfaces' held at the State University of Ghent, Belgium between August 28 and September 9, 1978. The aim of these lectures was to highlight some of the current progress in our understanding of the degenerate electron ’liquid’ in an external field which is neither uniform nor periodic. This theme brought together such topics as the electronic structure at metallic surfaces and in random metallic alloys, liquid metals and metallic glasses. As is the case in connection with infinite order ed crystals, the central issues to be discussed were the nature of the electronic spectra, the stability of the various phases and the occurrence of such phenomena as magnetism and supercon ductivity. In the theoretical lectures the emphasis was on detailed rea listic calculations based, more or less, on the density functional approach to the problem of the inhomogeneous electron liquid. How ever, where such calculations were not available, as in the case of magnetism in random alloys and that of metallic glasses, sim pler phenomenological models were used. The theoretical discussions were balanced by reviews of the most promising experimental techniques. Here the stress was on results and their relevance to the fundamental theory. lforeover, the attention had centered on those experiments which probe the electronic structure in the greatest detail.
