The mathematician John Pell was a member of the Royal Society and one of the generation of scientists that included Boyle, Wren, and Hooke. Although he left a huge body of manuscript materials, he has remained a neglected figure, whose papers have never been properly explored. This book is a full-length study of Pell and presents an in-depth account of his life and mathematical thinking based on a detailed study of his manuscripts. It also brings to life a strange, appealing, but awkward character, whose failure to publish his discoveries was caused by powerful scruples. In addition, this book shows that the range of Pell's interests extended far beyond mathematics. He was a key member of the circle of the ‘intelligencer’ Samuel Hartlib; he prepared translations of works by Descartes and Comenius; in the 1650s he served as Cromwell's envoy to Switzerland; and in the last part of his life he was an active member of the Royal Society, interested in the whole range of its activities. The study of Pell's life and thought thus illuminates many different aspects of 17th-century intellectual life. The book is in three parts. The first is a detailed biography of Pell; the second is an extended essay on his mathematical work; the third is a richly annotated edition of his correspondence with Sir Charles Cavendish. This correspondence, which has often been cited by scholars but has never been published in full, is concerned not only with mathematics but also with optics, philosophy, and many other subjects. Conducted mainly while Pell was in the Netherlands and Cavendish was also on the Continent, it is a fascinating example of the correspondence that flourished in the 17th-century ‘Republic of Letters’.