1 More than thirty years after its discovery by Abraham Robinson, the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum, as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line...