For the purposes of a course on mysticism, the important works are the Divine Names and the Mystical Theology. "Names", in the title of the first work, means "predicates". In other words, what can we say about God? If we are going to think about God in positive terms, we must use only those terms sanctioned by scripture. There are lots of these. He gives us a partial list: good, fair, wise, beloved, God of Gods, Lord of Lords, Eternal, Existent, Creator of Ages, Wisdom, Mind, Power, Ruler, a Star, a fire, water, a wind, a spirit, a dew, a cloud, all creation, etc.
Dionysius wants to say, though, that we must go beyond this. There are three points of view we can adopt when talking about God:
1. We can talk about God as he is in himself. But in himself he is "beyond all speech". So, we can affirm nothing of God. No predicate truly applies to him. All we can do is deny predicates of God. This is the project of the Mystical Theology.
2. We can also talk about God as he is the cause of things (insofar as things proceed from him). If we call God a creator, we are not talking about his inner nature, but about his relationship to other things. We are "naming" God in a backhanded way. This is the job of the later part of the Divine Names; the earlier parts set out this division.
3. We can talk about God in another "connotative" way, not as things proceed from God, but as they return to him. This is the business of the two books on the Hierarchies.
This is all in chapter 1 of Divine Names. He carries on by considering the names of God. Problem: since God is not complex, any name will refer to all of God. If that is true, it seems to risk destroying the Trinity, because it makes it a trinity only from our point of view. Answer: Dionysius distinguishes between two types of names:
a) Undifferentiated (unified, common): These refer to the entire Godhead. There are two kinds:
i) Names like "super excellent", "super divine", "super essential", and all those titles wherein the negative expresses an excess. These terms are discussed more in the Mystical Theology. This is called Apophatic theology, or the way of remotion (removing), or the negative way (via negativa).
ii) All those titles that have a causal sense: good, fair, existent, wise, and whatever titles are ascribed to the Cause of all good things from its bountiful gifts. This is called Cataphatic theology, or later, the way of attribution, or the positive way.
b) Differentiated: These refer to one person of the Trinity.
The idea here is that the terms that apply equally to all three persons of the trinity are the terms that relate God in some way to creation. The terms that apply to one of the persons of the trinity are only within the Trinitarian theory itself, with one exception: incarnation.
It is all quite untidy. And, it doesn't even really answer the question, if God is simple. In the rest of the Divine Names, Dionysius goes through the undifferentiated names of type a.ii.
Note the influence of Plotinus, though. As one approaches the one, it becomes dark. There is apophatic theology. You can't talk about God. Dionysius does think that God exists, but on an entirely different ontological plane than us.
One of the points of contact that makes the hierarchies possible is the henads. This is a development on Plotinus. Just as for Plotinus individual souls participate in the Soul, and individual intelligences participated in the Intelligence, so too there is something that participates in the One without changing it, and it makes possible movement in the One without introducing change. These are called the henads (from "unified"). Notice that this introduces Greek ideas into Christian theology, and muddies the waters of the distinction between Creator and created. Dionysius is insistent that there is a distinction, but he also needs something that makes the mystical path worth taking. And, he doesn't want to take Augustine's route, of finding the Imago Dei.