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An algebraic specification is a description of one or more abstract data types. There are three main semantic approaches to algebraic specifications: (1) the initial algebra approach, (2) the terminal algebra approach, and (3) the loose approach. A fourth approach that is mainly of theoretical interest uses iso-initial algebras. This chapter reviews the basic concepts for the theory of algebraic specifications. It also describes the notion of an abstract data type and discusses its basic properties. The chapter also describes four other semantic concepts and algebras for specifying nondeterminism and concurrency. The chapter discusses the existence of initial and terminal algebras, the lattice structure of the models, and the expressive power of initial and terminal algebra specifications. The chapter also presents two additional concepts for algebraic specifications, which are both practically and …