William Petty (1623-1687) was a key figure in the English colonization of Ireland, the institutionalization of experimental natural philosophy, and the creation of social science. Examining Petty's intellectual development and his invention of 'political arithmetic' against the backdrop of the European scientific revolution and the political upheavals of Interregnum and Restoration England and Ireland, this book provides the first comprehensive intellectual biography of Petty based on a thorough examination not only of printed sources but also of Petty's extensive archive and pattern of manuscript circulation. It is also the first fully contextualized study of what political arithmetic - widely seen as an ancestor of modern social and economic analysis - was originally intended to do. Ted McCormick traces Petty's education among French Jesuits and Dutch Cartesians, his early work with the 'Hartlib Circle' of Baconian natural philosophers, inventors, and reformers in England, his involvement in the Cromwellian conquest and settlement of Ireland, and his engagement with both science and the politics of religion in the Restoration. He argues that Petty's crowning achivement, political arithmetic, was less a new way of analysing economy or society than a new 'instrument of government' that applied elements of the new science - a mechanical worldview, a corpuscularian theory of matter, and a Baconian stress on empirical method and the transformative purposes of natural philosophy - to the creation of industrious and loyal populations. Finally, he examines the transformation Petty's program of social engineering, after his death, into an apparently apolitical form of statistical reasoning.