This volume gives an up-to-date overview of theoretical and experimental methods of studying the electronic band structure. Various formalisms for explicit calculations and many details of useful applications, particularly to alloys and semiconductors, are presented. The contributions cover the following subjects: alloy phase diagrams, density functionals; disordered alloys; heavy fermions; impurities in metals and semiconductors; linearize band structure calculations; magnetism in alloys; modern theory of alloy band structure; momentum densities in metals and alloys; photoemission; quasi-particles and properties of semiconductors; the recursion method and transport properties of crystals and quasi-crystals.