This project, which is based on a course that Ahmed Ragab and I co-teach in the Department of the History of Science at Harvard, will yield a co-authored book for the use of students and nonspecialist scholars. This will present scientific and medical thought and practice in the Islamic and Latin Christian Middle Ages as a unified enterprise with a unified history, rather than as part of a story describing the transfer of knowledge from Greek antiquity to early modern Europe via the Arabic-speaking world. The book is organized around the exchange and circulation of people, objects, texts, and information within and between the two cultures, with special attention to social, cultural, and religious context. We have organized our exposition into three chronological sections. The first discusses science in relation to diplomatic missions, commercial contacts, and individual travel in the early Middle Ages, focusing on relations between the Carolingian Empire, the Abbasid Empire, and the Umayyad Emirate from the mid-eighth through tenth centuries. The second explores the flowering of Arabic, Latin, and Hebrew scientific and medical knowledge in the Mediterranean territories that moved back and forth between Muslim and Christian domination over the course of the eleventh through early thirteenth centuries in the Iberian peninsula, Sicily, southern Italy, and the Crusader states. The third traces the gradual disappearance of the scientific “trading zones” of the Mediterranean and the emergence of a more polarized relationship between “Eastern” and “Western” cultures of knowledge in the later thirteenth through fifteenth centuries.