This paper explains Sebastián Izquierdo's (1601-1681) theory of priority. Izquierdo was a seventeenth-century Spanish scholastic philosopher who was best known in the seventeenth century for his ambitious work, Pharus Scientiarum (“Lighthouse of the Sciences”), which attempts to carry out the Baconian project of establishing a universal art of acquiring and disseminating knowledge. Disputation 15 of the Pharus contains one of the most detailed treatments of priority in the history of philosophy. The purpose of this paper is to limn the contours (...) of that theory. Taking Aristotle as a source of inspiration, Izquierdo distinguishes between absolute and relative priority, and the former he divides into priority of duration, priority of worth, priority of origin, and priority of non-mutual connection. These priorities can also be “chained” and “mixed” in various ways. The task for Izquierdo is to explain what unifies the various priority relations: why do they all count as instances of a single phenomenon (or do they)? I argue that Izquierdo answers this question by means of his notion of a series, which is central to his theory of priority. I explain what a series is, and I explain how Izquierdo’s entire theory of priority is generated from his notion of a series. In the end, Izquierdo’s theory is admirably simple, yet remarkably flexible and able to accommodate a wide variety of priority claims. (shrink)