The theory of surface states underlies our knowledge of the behavior of electrons at solid surfaces, which is of paramount importance in understanding the mechanisms by which solid-state devices operate and catalytic reactions proceed. In this work, the subject is viewed through the "theoretical eye" of a physicist, but the topics are treated in an elementary fashion. The main features of the presentation are its instructive, model-based approach; detailed step-by-step derivations of the equations; smooth progression through the simple wave-function matching techniques to the more sophisticated Green-function methods; and the historical theme, which traces the evolution of the subject from its founding by the Nobel Laureate Igor Tamm in 1932, through the invention of the transistor in 1947 by Schockley, Bardeen and Brattain, to recent developments. The book will appeal to both theoretical and experimental surface scientists from chemistry, materials science, and electronic engineering.