This paper provides an overview of initial algebra semantics, a unified approach to specifying formal semantics of programming languages. The key concept is that an algebra \( S \) is *initial* in a class \( C \) of algebras if for every \( A \) in \( C \), there exists a unique homomorphism \( h_A : S \rightarrow A \). The paper discusses the importance of many-sorted algebras and their role in handling abstract syntax, where the initial algebra approach is implicit. It also introduces continuous algebras, which extend the applicability of initial algebra semantics by combining algebraic insights with lattice-theoretic ideas. The paper includes examples and applications, such as context-free grammars and denotational semantics, to illustrate the concepts and their practical use in programming language semantics. The authors aim to expose the surprising unity in the apparent diversity of approaches to formal semantics.This paper provides an overview of initial algebra semantics, a unified approach to specifying formal semantics of programming languages. The key concept is that an algebra \( S \) is *initial* in a class \( C \) of algebras if for every \( A \) in \( C \), there exists a unique homomorphism \( h_A : S \rightarrow A \). The paper discusses the importance of many-sorted algebras and their role in handling abstract syntax, where the initial algebra approach is implicit. It also introduces continuous algebras, which extend the applicability of initial algebra semantics by combining algebraic insights with lattice-theoretic ideas. The paper includes examples and applications, such as context-free grammars and denotational semantics, to illustrate the concepts and their practical use in programming language semantics. The authors aim to expose the surprising unity in the apparent diversity of approaches to formal semantics.