This book presents a unifying approach to semantical concepts and deductive methods used in recursive, equational and logic programming, data type specification and automated theorem-proving. The common background is Horn logic with equality. Although this logic does not cover the full first-order logic, it supplies us with a language that allows "natural" problem specifications, offers several semantical views (functional, relational, inductive, behavioural, etc.) and puts at our disposal a number of more or less special-purpose deductive methods, which can be used as rapid prototyping tools. The Horn clause calculus serves as the interface between the model-theoretic concepts of initial semantics, final semantics and internalized logic on one hand and deductive methods based on resolution, paramodulation, reduction and narrowing on the other hand. This contrasts previous approaches, which equip each semantical concept with its own calculus or, conversely, build a particular semantics upon each deductive method. Here the author starts out from the Horn clause calculus and develops individual concepts, results and procedures in a way that clearly delimits their respective purposes from each other. The unifying approach also brings about new variants or generalizations of known results and admits comparable arguments in soundness and completeness proofs.