This paper presents an overview of initial algebra semantics, a framework for specifying formal semantics of programming languages. The key concept is that an algebra S is initial in a class C of algebras if there exists a unique homomorphism from S to any other algebra A in C. This concept is used to unify the treatment of iterative and recursive semantic features in the same framework as more basic operations. The paper discusses the use of initial algebra semantics in various contexts, including context-free grammars, denotational semantics, and syntax-directed translation. It also introduces the concept of continuous algebras, which extend the applicability of initial algebra semantics by combining algebraic insights with order-theoretic ideas. The paper provides a detailed discussion of many-sorted algebras, their properties, and their applications in programming language semantics. It also presents several examples of initial algebra semantics, including the semantics of context-free grammars and the semantics of a simple applicative language. The paper concludes with a discussion of the relationship between initial algebra semantics and other approaches to formal semantics, and it highlights the importance of initial algebra semantics in providing a unified framework for understanding the semantics of programming languages.This paper presents an overview of initial algebra semantics, a framework for specifying formal semantics of programming languages. The key concept is that an algebra S is initial in a class C of algebras if there exists a unique homomorphism from S to any other algebra A in C. This concept is used to unify the treatment of iterative and recursive semantic features in the same framework as more basic operations. The paper discusses the use of initial algebra semantics in various contexts, including context-free grammars, denotational semantics, and syntax-directed translation. It also introduces the concept of continuous algebras, which extend the applicability of initial algebra semantics by combining algebraic insights with order-theoretic ideas. The paper provides a detailed discussion of many-sorted algebras, their properties, and their applications in programming language semantics. It also presents several examples of initial algebra semantics, including the semantics of context-free grammars and the semantics of a simple applicative language. The paper concludes with a discussion of the relationship between initial algebra semantics and other approaches to formal semantics, and it highlights the importance of initial algebra semantics in providing a unified framework for understanding the semantics of programming languages.