The chapter introduces the concept of evolving algebras (EAs) as a versatile machine for simulating arbitrary algorithms in a direct and coding-free manner. EAs are defined as multi-sorted structures with partial operations, allowing quantifier-free formulas as terms. The chapter covers static algebras, which are structures without relations, and sequential evolving algebras, which include basic transition rules and methods for importing new elements. It discusses the extension of sequential EAs to handle nondeterministic behavior and introduces parallel and distributed EAs. The chapter also explores the use of variables in parallel EAs and the concept of runs, which are sequences of states obtained by executing programs. The text emphasizes the importance of logic simplicity and pragmatic considerations in the design of EAs, and it provides examples and applications of EAs in specifying languages, architectures, and protocols.The chapter introduces the concept of evolving algebras (EAs) as a versatile machine for simulating arbitrary algorithms in a direct and coding-free manner. EAs are defined as multi-sorted structures with partial operations, allowing quantifier-free formulas as terms. The chapter covers static algebras, which are structures without relations, and sequential evolving algebras, which include basic transition rules and methods for importing new elements. It discusses the extension of sequential EAs to handle nondeterministic behavior and introduces parallel and distributed EAs. The chapter also explores the use of variables in parallel EAs and the concept of runs, which are sequences of states obtained by executing programs. The text emphasizes the importance of logic simplicity and pragmatic considerations in the design of EAs, and it provides examples and applications of EAs in specifying languages, architectures, and protocols.