In the previous chapter of the Categories we have already discussed homonymy, synonomy, and paronymy. This section, Chapter 2 of Aristotle’s Categories, sets forth a four-fold system of classification for “things that are,”  in addition to introducing a distinction between things that are said “in combination” and things said “without combination.” Although not without straying interpretations, the distinction between “combined and uncombined” is rather clear, on my view, from the context. So I will instead be focusing on the four-fold division that takes up the majority of the chapter and the lion’s share of the philosophical difficulty. Needless to say, however, for the purpose of an explanatory post such as this, I will be sticking to orthodox and traditional interpretations, although of course there are always divergences and minority reports.
Things That Are Said:
Of the things that are said, some are said in combination (symploke), while some are said without combination. Those that are said in combination are such as “human runs,” “human wins.” Those without combination are such as “man,” “ox,” “runs,” “wins.”
Things That Are:
A) Of things that are, some are said of an individual subject (tis hypokeimenon), but are not in any subject, such as “human” is said of an individual human, but is not in any subject.
B) But some are in a subject, yet are said of no subject. And by “in a subject,” I mean that which exists in something not as a part and is impossible to be apart from that in which it is. For example, an individual grammatical knowledge (tis grammatike) is in a subject, but is said of no subject, and individual white is in a subject, i.e. a physical body (for every color is in a body) but it is said of no subject.
C) Some are said both of a subject and are in a subject, for example knowledge (episteme) is in a subject, i.e. a soul, but is said of a subject, i.e. grammatical knowledge
D) Some are neither in a subject nor said of a subject, for example, an individual person or an individual horse–– for none of these is in a subject nor is it said of a subject. And generally, things that are irreducible and one in number are said of no subject, but nothing hinders some things from being in the subject. For, of the things in a subject, the individual grammatical knowledge is one of them (Aristotle, Categories, 1a16-1b9). 
First let us discuss what Aristotle means by “in a subject” and “said of a subject.” Since the four-fold division consists entirely in affirming or denying these classifications, resulting in four distinctions, if we understand these two phrases, we are well on our way to understanding all of this chapter.
The In-a-subject Relation
It is best to understand both the in-a-subject and said-of-a-subject distinctions, at a general level, as belonging to relations between things. So in-a-subject means that if X is in Y, where Y is the subject, we are to understand Y as either a substance proper or, more abstactly, as that thing, whatever it is, which undergoes the process which results in some relation. X here cannot exist independently from some kind of subject or substance, and that is why it is said to be “in” a subject, for it will not exist “out” of a subject. Thus the category of things not a subject or substance, here represented by X, are dependent on the subject for their existence. So in Aristotle’s example, an individual’s grammar-knowledge (his understanding of how language works) is “in” an individual (his mind) because it is dependent on the individual and cannot exist apart from this individual, viz., Grammatical knowledge is in the mind.
The Said-of-a-subject Relation
While the in-a-subject distinction concerns a subject or substance and its independent status (in contrast to the dependent relation of a non-subject or non-substance), the said-of-a-subject relation pertains to an individual and a universal, or in slightly different wording, to an individual and a species or genus. Returning to one of Aristotle’s examples, the term human (as a species) is “said of” an individual human, viz., Socrates is a human.
The Four-fold Division Simplified
Now that we have discussed the in-a-subject relation and the said-of-a-subject relation, we can apply these distinctions to the text above to get four categories into which (presumably) all things fit.
A) Essential Universals: Universals (or species and genera) in their relation to substances. E.g. “Human” in “Socrates is human.”
B) Accidental Particulars: Particulars, but not substances. E.g. An individual grammatical knowledge in a person.
C) Accidental Universals: Universals (or species and genera) in their relation to things other than substances. E.g. Knowledge is said both of grammatical knowledge (i.e. grammatical knowledge is knowledge) and is in a subject, i.e. a mind.
D) Primary Substances: Particulars that are substances. E.g. An individual such as Socrates or a particular horse, e.g. Secretariat
 Although the division is four-fold, there are actually 6 possibilities; however two of these possibilities are contradictions: “in a subject and not in a subject” and “of a subject and not in a subject.”
 Τῶν λεγομένων τὰ μὲν κατὰ συμπλοκὴν λέγεται, τὰ
δὲ ἄνευ συμπλοκῆς. τὰ μὲν οὖν κατὰ συμπλοκήν, οἷον
ἄνθρωπος τρέχει, ἄνθρωπος νικᾷ· τὰ δὲ ἄνευ συμπλοκῆς,
οἷον ἄνθρωπος, βοῦς, τρέχει, νικᾷ.
Τῶν ὄντων τὰ μὲν καθ’ ὑποκειμένου τινὸς λέγεται, ἐν (20)
ὑποκειμένῳ δὲ οὐδενί ἐστιν, οἷον ἄνθρωπος καθ’ ὑποκειμένου
μὲν λέγεται τοῦ τινὸς ἀνθρώπου, ἐν ὑποκειμένῳ δὲ οὐδενί ἐστιν·
τὰ δὲ ἐν ὑποκειμένῳ μέν ἐστι, καθ’ ὑποκειμένου δὲ οὐδενὸς
λέγεται, —ἐν ὑποκειμένῳ δὲ λέγω ὃ ἔν τινι μὴ ὡς μέρος
ὑπάρχον ἀδύνατον χωρὶς εἶναι τοῦ ἐν ᾧ ἐστίν,— οἷον ἡ τὶς (25)
γραμματικὴ ἐν ὑποκειμένῳ μέν ἐστι τῇ ψυχῇ, καθ’ ὑπο-
κειμένου δὲ οὐδενὸς λέγεται, καὶ τὸ τὶ λευκὸν ἐν ὑποκειμένῳ
μέν ἐστι τῷ σώματι, —ἅπαν γὰρ χρῶμα ἐν σώματι,— καθ’
ὑποκειμένου δὲ οὐδενὸς λέγεται· τὰ δὲ καθ’ ὑποκειμένου τε
(1b.) λέγεται καὶ ἐν ὑποκειμένῳ ἐστίν, οἷον ἡ ἐπιστήμη ἐν ὑπο-
κειμένῳ μέν ἐστι τῇ ψυχῇ, καθ’ ὑποκειμένου δὲ λέγεται
τῆς γραμματικῆς· τὰ δὲ οὔτε ἐν ὑποκειμένῳ ἐστὶν οὔτε καθ’
ὑποκειμένου λέγεται, οἷον ὁ τὶς ἄνθρωπος ἢ ὁ τὶς ἵπ-
πος, —οὐδὲν γὰρ τῶν τοιούτων οὔτε ἐν ὑποκειμένῳ ἐστὶν (5)
οὔτε καθ’ ὑποκειμένου λέγεται·— ἁπλῶς δὲ τὰ ἄτομα καὶ ἓν
ἀριθμῷ κατ’ οὐδενὸς ὑποκειμένου λέγεται, ἐν ὑποκειμένῳ δὲ
ἔνια οὐδὲν κωλύει εἶναι· ἡ γὰρ τὶς γραμματικὴ τῶν ἐν ὑπο-