This is a survey of Aristotle's development of the concept of substance in the Categories and Book VII (Zeta) of the Metaphysics. We begin with the Categories conception of a primary substance as that which is not "in a subject" -- i.e., not ontologically dependent on anything else -- and also not "said of a subject" -- i.e., not predicated of any item beneath it in its categorial tree. This gives us the idea of primary substances as ontologically (...) basic individuals, the fundamental subjects of predication and of change. We then examine the conception of substance in Metaphysics Zeta, where Aristotle is interested not just in the question of what the primary substances are, but in the question of what makes them substances, or, as he would put it, what the "substance OF something" is. The conception of substance that Aristotle ends up with seems (as has been frequently noted) to be threatened with inconsistency, in that Aristotle seems to want to maintain, simultaneously, that (i) substance is form, (ii) form is universal, and (iii) no universal is a substance. Two main approaches toward resolving this inconsistency are considered, and a sketch is provided of how one of these approaches might be fleshed out. On the line I propose, the substantial form of a material compound is predicated accidentally and universally of the matter of that compound, but it is not the substance of the matter of which it is predicated. Rather, it is the substance of itself; but since it is the cause of the compound's being essentially the kind of thing that it is, the substantial form is, in a derivative way, the substance of the compound as well. (shrink)