This unique book shows how chemistry and physics come together in the solid state and on surfaces. Using a lively, graphic, descriptive approach, it teaches chemists the language that is necessary to understand the electronic structure of extended systems. And, at the same time, it demonstrates how a chemical, frontier-orbital, approach to solid state and surface bonding and reactivity may be constructed. The book begins with the language of crystal orbitals, band structures and densities of states. The tools for moving back from the highly delocalized orbitals of the solid are then built up in a transparent manner; they include decompositions of the densities of states and crystal orbital overlap populations. Using these tools, the book shapes a meeting ground between detailed quantum mechanical calculations and a chemical frontier orbital perspec- tive. Applications include a general picture of chemisorption, bond-breaking and making in the solid state, bonding in metals, the electronic structure of selected conducting and supercon- ducting structures, dissociation, migration and coupling on surfaces and the forces controlling deformation of extended systems.