This monograph is an annotated translation of what is considered to be the world first calculus textbook, originally published in French in 1696. That anonymously published textbook on differential calculus was based on lectures given to the Marquis de l’Hôpital in 1691-2 by the great Swiss mathematician, Johann Bernoulli. In the 1920s, a copy of Bernoulli lecture notes was discovered in a library in Basel, which presented the opportunity to compare Bernoulli notes, in Latin, to l’Hôpital text in French. The similarities are remarkable, but there is also much in l’Hôpital book that is original and innovative. This book offers the first English translation of Bernoullis notes, along with the first faithful English translation of l’Hôpital text, complete with annotations and commentary. Additionally, a significant portion of the correspondence between l’Hôpital and Bernoulli has been included, also for the fi rst time in English translation. This translation will provide students and researchers with direct access to Bernoulli ideas and l’Hôpital innovations. Both enthusiasts and scholars of the history of science and the history of mathematics will fi nd food for thought in the texts and notes of the Marquis de l’Hôpital and his teacher, Johann Bernoulli.