This programme aims to stimulate the theoretical study of spectral properties of partial differential operators which is a subject with many practical applications. Among them are problems appearing in solid state physics, superconductivity, problems cons erning stability of matter, telecommunication, etc. Stimulated by these and others applications this area of mathematical physics contains many outstanding difficult problems which mathematicians have been trying to solve during many decades. Recent progr ess in solving some of these problems is a major motivation for joining forces with different European research groups.