Abstract: This monograph derives from the integration of lecture notes developed by the authors in the last three years. The topics considered include: simply typed lambda-calculus, PCF, categorical interpretations, domains of algebraic complete partial orders, adequacy results, partial orders, adequacy results, partial lambda-calculus, continuations, domain equations, dependent and second-order types, semantics of polymorphism, stability and realizability. As a course support we offer two appendices on recursion theory and category theory.