Nonstandard techniques in real analysis (Q1097981)

As stated in the introduction the purpose of the paper under review is to present the techniques of nonstandard analysis in simple terms to make them readily available to those working in the field of analysis. Apart from the introduction the paper is divided into the following sections: 2. Hyperreal numbers, 3. Operating in \({}^*{\mathbb{R}}:\) The transfer principle, 4. Superstructures and universes: The internal set distinction, 5. Languages and the star operation, 6. New applications: Locally valid suborderings, 7. Concurrent relations, 8. Metric and topological spaces: Extensions of infinitesimally valid properties, 9. Saturation: Application to nonstandard path continuity. It is the reviewer's opinion that the author has succeeded well in explaining the main aspects of the techniques of nonstandard analysis. We can recommend it warmly to anyone who is interested in getting acquainted with these new model theoretic techniques.