On the Categories (ca. 350 BCE), which purports to describe all the types of entities that exist. The participants are Mark, Wes, and Dylan.
The most important of these Categories is substance, a term which primarily picks out individual natural things (a particular person, animal, plant, or material) and secondarily picks out the kinds that group those things (e.g. the species person and its genius animal). The rest of the categories (quality, quantity, relative, where, when, being-in-a-position, having, doing, and being affected) are all types of being rely on their being substances.
So why does Aristotle break down the world the way he does (in this text; note that he actually has a very different notion of substance in his presumably later account in the Metaphysics)? Why are species descriptions "secondary substances" instead of qualities? What makes for a substance (the Greek word translated as substance literally just means "being"), and how do qualities and the rest of the categories actually relate to these substances? Aristotle's use of the term "relative" instead of "relation" (which sounds like things insofar as they are related instead of the relation) gives us a possible hint that he may actually still be talking about substances when talking about the rest of the categories, like substances are all that exist, but there are different aspects of substances we can focus on, different ways in which we can apprehend them. So if you take a single person (say Socrates), there are many types of things one can say about him at any given time; what are those types?
A complicating issue is the structure of the text: All the consideration of the categories is in the middle part of the text (The "Predicamenta"), and it's debated why the parts before and after that are actually part of this text at all. So we start near the beginning (in the "Pre-Predicamenta") considering how entities might be "present in" or "said of" other entities. Universals are said of substances, so for instance Socrates is a person and Socrates is wet. Accidental properties are present in substances: If Socrates is wet, then there's wetness in him, both in the sense that there's an individual instance of wetness in him and thereby they universal wetness is also in him, if that makes sense. However, since personhood is not an accidental property but the essence of Socrates, then while personhood is said of Socrates, there's no personhood in Socrates. The individual Socrates is according to this terminology neither in nor said of anything else, and that's what makes it a primary substance: It's a self-subsistent entity, not relying on other entities to exist.
You can probably see places in this scheme that later thinkers might object to. Is there really such a difference in the dependent existence of a substance vs. a property? Yes, Aristotle seems right (contra Plato) that there can be no "wetness" without something in the world that is wet, but it's also true that everything existent has some level of wetness or other, even if that level is zero, and so in that sense every substance relies on every property. This might be easier to see with color or shape: Surely colors and shape don't exist independently of colored objects, but all objects have some color and shape or other.
Aristotle's special treatment of species and genus as secondary substances is also very strange. Why insist that there's an individual instance of wetness (what in our recent Hegel episode we called a "sensory particular") in wet objects, but not that there's an individual instance of personhood in all people? Isn't being a person just a bunch of properties like having a certain appearance and/or genetic make-up and/or behavior? Isn't that genetic make-up quite literally in the person? Isn't this distinction between "present in" and "said of" pretty strange and arbitrary?
There's also the related question of artifacts: Why is being a person a description of the substance of a thing but being a hammer is not? Something's being a hammer will have to be a relation of some substance to human intentions, meaning that there are not literally hammers, but there are things that we use as hammers, and so presumably on Aristotle's account we'd have to give a description of something's being a hammer in terms of its being affected in some way, but Aristotle tells us almost nothing about those latter categories like affection in this text, so there's no real way we can tell.
In the Metaphysics, we'll move to Aristotle's more famous view that an individual is not the basic kind of thing, but that every individual has form and matter, so that the "personhood" would be the form, and this particular flesh is the matter of Socrates. Even this view is quite different than our modern view that the basic components of things are the smallest bits, whether they be elements or atoms or quarks or super-strings, or what have you. Why insist that the ways in which it's useful for us to break up the world for common-sense purposes are metaphysically basic? A common interpretation of the Categories is that it's both an analysis of the basic types of things and an analysis of parts of speech, because the world as it is independent of our minds is exactly isometric to the world as we perceive and talk about it. Why would we want to make that assumption?
Get the J.L. Ackrill translation most of us read or try it online. Alternately, buy the Loeb version that Dylan used. There's also a Librivox version if you'd prefer to listen, though the reader's choice to render out loud every use of quotation marks (despite the fact that these were clearly not in the Greek) makes a good chunk of it absolutely maddening.
A great introduction is the Stanford Encyclopedia of Philosophy article written by Paul Studtmann. Wes also recommends John Vella's Aristotle: A Guide to the Perplexed and Jonathan Lear's Aristotle: The Desire to Understand. Mark checked out Dan Bonevac's lecture on the topic as well as an interesting podcast interview on the book with Joseph Hattrup.