What is it, metaphysically, for a universal to be instantiated in a concrete particular, or for a concrete particular to instantiate a universal? What is an instantiated universal to that universal? Philosophical discussion around these questions has been ongoing since the beginning of philosophy itself, and the relevant literature is more than vast. Aristotle is usually thought to be the ‘culprit’: the one who created the ‘problem’, but positing that his universals are immanent, i.e. instantiated in concrete particulars. But what does this mean, metaphysically? The mainstream interpretation of Aristotle’s position is that according to which universals are instantiated by ‘combining’ somehow with matter, understood as a primitive bare particular. There are at least three issues with this mainstream interpretation of Aristotle’s position that fly in the face of modern metaphysics and make it, thus understood, unappealing and objectionable. Primitive bare particulars are generally considered an unwelcome addition to the ontology. Further, Aristotelian matter is seen as a suspicious entity, even by nowadays’ neo-Aristotelians. Finally, conceiving of instantiation in terms of a universal ‘combining’ with matter suggests that instantiation is a relation; while there are many positions on the table as to which kind of relation that might be, the very hypothesis that instantiation is (on this interpretation) a relation has attracted much criticism. In this course, we will examine the ‘origins’ of the problem of instantiation of universals in Plato’s metaphysics, and its background in Anaxagoras’s metaphysics; and then come to study Aristotle’s position.