What are the three hypostases?

Plotinus, answered from the texts and cited to the page.

Plotinus answers

The three are to Hen (the One), Nous (Intellect), and Psychê (Soul) — and between them they constitute the whole order of real being, admitting neither more nor fewer.¹ Begin with Nous. The Intellectual-Principle is a manifold, not a simplex: its intellective act establishes Being, which in turn becomes the cause of that very intellection, so that Intellect and Being are coalescent, two-sided, never apart.²

The primal categories — Intellectual-Principle, Existence, Difference, Identity, Motion, Rest — all arise within this second hypostasis; Number and Quantity follow from its manifold character, and Quality from the specific character of each Idea standing as a principle.³ Yet the Divine Mind in its mentation thinks itself; Thinker and Thought are one, and in this primal knowing it includes, as one and the same act, the knowledge of the knowing — so that no further multiplication of principles within Nous is warranted.⁴

Before Nous stands the One. Number, Quantity, is not primal; before even duality there must stand the unity.⁵ The One transcends knowing: knowing is a unitary thing but defined, whereas the first is One but undefined, and a defined One would not be the One-Absolute.⁶ Any affirmation is of a thing, and the all-transcending rests above even the most august divine Mind; we can give it no name because that would imply predication — we can but try to indicate, in our own feeble way, something concerning it.⁷

When we call it the Good we mean no more than to indicate it to ourselves in the best terms we find; it is self-sufficing not as a compound dependent on constituents but as deriving from nothing alien and entering into nothing alien.⁸ From the One proceeds Nous, and from Nous proceeds Psychê. The movement toward Nous or within it is already the realm of Soul's operation: a Reason-Principle emanates from Intellect and enters into Soul, making it an Intellectual Soul, but creating no intermediate principle to stand between the two.⁹

The entire intellectual order may be figured as a kind of light with the One in repose at its summit as its King — not identical with its source, yet not severed from it, seeing and knowing, the primal knower.¹⁰ Soul stands linked as a member of the divine unless by deliberate apostasy.¹¹ No other divine kinds are needed. Those who hold to fewer principles must identify either Intellect with Soul or Intellect with the First; those who multiply further cannot find principles at once simpler and more transcendent than these three.¹²

Sources

We need not, then, go seeking any other Principles; this — the One and the Good — is our First, next to it follows the Intellectual Principle, the Primal Thinker, and upon this follows Soul. Such is the order in nature. The Intellectual Realm allows no more than these and no fewer.
The Second and Third Enneads
Intellectual-Principle by its intellective act establishes Being, which in turn, as the object of intellection, becomes the cause of intellection and of existence to the Intellectual-Principle... Now while these two are coalescents, having their existence in common and are never apart, still the unity they form is two-sided.
The Fifth Ennead
The Intellectual Kosmos thus a manifold, Number and Quantity arise: Quality is the specific character of each of these ideas which stand as the principles from which all else derives.
The Fifth Ennead
The Divine Mind in its mentation thinks itself; the object of the thought is nothing external: Thinker and Thought are one; therefore in its thinking and knowing it possesses itself, observes itself and sees itself not as something unconscious but as knowing: in this Primal Knowing it must include, as one and the same Act, the knowledge of the knowing.
The Second and Third Enneads
Number, Quantity, is not primal: obviously before even duality, there must stand the unity.
The Fifth Ennead
Knowing is a unitary thing, but defined: the first is One, but undefined: a defined One would not be the One-Absolute: the absolute is prior to the definite.
The Fifth Ennead
Thus The One is in truth beyond all statement: any affirmation is of a thing; but the all-transcending, resting above even the most august divine Mind, possesses alone of all true being, and is not a thing among things; we can give it no name because that would imply predication.
The Fifth Ennead
When we speak of The One and when we speak of The Good we must recognise an Identical Nature... it is the Self-Sufficing only in the sense that it is not of that compound nature which would make it dependent upon any constituent... Deriving then, from nothing alien, entering into nothing alien, in no way a made-up thing, there can be nothing above it.
The Second and Third Enneads
With movement — towards it or within it — we are in the realm of the Soul's operation: such act is a Reason-Principle emanating from it and entering into Soul, thus made an Intellectual Soul, but in no sense creating an intermediate Principle to stand between the two.
The Second and Third Enneads
The entire intellectual order may be figured as a kind of light with the One in repose at its summit as its King... this, not identical with its source, is yet not severed from it nor of so remote a nature as to be less than Real-Being; it is no blind thing, but is seeing and knowing, the primal knower.
The Fifth Ennead
As a manifold, then, this God, the Intellectual-Principle, exists within the Soul here, the Soul which once for all stands linked a member of the divine, unless by a deliberate apostasy.
The Fifth Ennead
Those who hold to fewer Principles must hold the identity of either Intellectual-Principle and Soul or of Intellectual-Principle and The First... Now what other (Divine) Kinds could there be? No Principles of the universe could be found at once simpler and more transcendent than this whose existence we have affirmed and described.
The Second and Third Enneads