Written Principia on the Sentences of Peter Lombard constitute a largely unexplored but exciting genre that corresponds to a complex exercise imposed by the statutes of medieval universities throughout Europe during the 14th and 15th centuries. Although almost completely neglected by modern scholarship, the academic practice of Principia was successful, long-lived, and widespread in the late Middle Ages. It required candidates for the title of doctor to begin their defense with a public debate in which they had to reveal their scientific interests, display their erudition, and demonstrate their intellectual prowess in the presence of a large audience. Before and during their Principia lectures, each candidate for the doctoral degree chose a topic that would exhibit his knowledge and innovation. Through debate with his colleagues in front of the staff and students of the faculty of theology and other members of the university or reputable persons (in Vienna the chancellor and the duke could participate in the debate and in Heidelberg the stuff of all the faculties from the body of the university), the candidate was expected to employ new methods and explore new paths. In most cases the discussion exceeded the confines of theology strictly speaking and allowed the candidates to indulge their interdisciplinary interests, since the debaters (the authors) combined science, mathematics, ethics, politics, astrology, literature, and so on in their polemics. Thus Principia or principial debates represent the cutting edge method to promote research in late-medieval universities. This volume aims to open a vast and advanced area of investigation by focusing on the principia practice that linked together medieval universities from different geographical and cultural contexts: Bologna, Cracow, Florence, Heidelberg, Oxford, Paris, Prague, Vienna.