Lectures on the Hyperreals

This is an introduction to nonstandard analysis based on a course of lectures given several times by the author. It is suitable for use as a text at the beginning graduate or upper undergraduate level, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions, a source of new ideas, objects and proofs, and a wellspring of powerful new principles of reasoning (transfer, overflow, saturation, en largement, hyperfinite approximation etc.).