Between the early 1987s and the 1961 publication of Abraham Robinson's celebrated work on non-standard analysis there emerged a large, diverse, technically deep and philosophically pregnant body of consistent (non-Archimedean) mathematics concerned with the infinitely large and infinitely small. This important body of work has continued to grow in recent decades, producing a number of truly major accomplishments. The central aims of the project are to examine the historical development of this line of research, exploring its implications for the theory of measurement and the philosophy of space and time.