The basic properties and results about computable functions (e.g., universality theorems) and semicomputability (e.g., definability) are treated in detail.

There is a study of computable functions on algebras of real numbers. This is generalised to a new account of functions that are computable and computably approximable on topological partial algebras.

A survey of other models of computation and appropriate
equivalence theorems for abstract algebras is provided.
Also included are accounts of connections with the theories
of computable algebra and computable analysis, and a short
history of generalisations of computability theory to
algebras.

**Contents**

- Introduction
- Signatures and algebras
- `While' computability on standard algebras
- Representation of semantic functions; Universality
- Notions of semicomputability
- Examples of semicomputable sets of real and complex numbers
- Computation on topological partial algebras
- A survey of models of computability