Saint Augustine’s De Trinitate (On The Trinity) is perhaps the first book-length treatment of the Holy Trinity. His starting point for understanding this mystery is faith (De Trinitate I.1). In fact, throughout the work Augustine grounds his epistemology ("epistemology" = how we know God) in his understanding of Isaiah 7:9 (VII.12; XV.2). That is, in order for us to understand the Trinity rightly, we must submit ourselves to the Almighty, plead for his mercy, and abstain from all sin. He writes in Book IV that “if this is difficult to understand, then you must purify your mind with faith, by abstaining more and more from sin, and by doing good, and by praying with the sighs of holy desire that God will help you to make progress in understanding and loving” (De Trinitate, IV.31).
Augustine's Chief Analogy: The “Mind”
Augustine’s chief creaturely metaphor for describing the Trinity is the mind. Within the mind, Augustine notes memory, understanding, and will. Each of these three are distinct entities per se, yet each of these “is the product of all three” (De Trinitate IV.30). As such, God has given us minds wherein we “might perceive in our memory, understanding and will that God is a trinity,” and that our minds are “that by which even the eternal and unchanging nature [of God] can be recalled, beheld and desired—it is recalled by memory, beheld by intelligence, and embraced by love [i.e., will or volition]” (XV.39).
Augustine argues that remembering, understanding, and willing share the same substance. And yet, these three beings in the mind are still distinct. He elaborates in §X.18 by showing that recalling (i.e., willing) a memory to mind requires an existing memory per se (i.e., understanding); if a memory is non-existent it is because the person is ignorant of that which is (perhaps) understandable. Therefore, if that which is understandable isn’t understood, the person can neither remember or will to remember it. And if it cannot be remembered in the mind, how can one will to remember it?
For Augustine, understanding and memory are encapsulated in the will (or love or volition) while one uses (i.e., wills or loves) the entirety of that which is understood and remembered (the very act of understanding). “Therefore, since they are each and all wholly contained by each, they are each and all equal to each and all, and each and all equal to all of them together, and these three are one, one life, one mind, one being” (X.18).
Augustine and Jonathan Edwards
In Johnathan Edwards’s Discourse on the Trinity, Edwards argues that since God is “infinitely happy in the enjoyment of himself, in perfectly beholding and infinitely loving, and rejoicing in, his own essence and perfections,” it follows that God must have “a most perfect idea of himself.” And so, God the Father beholds himself (i.e., he has a “most perfect idea of himself”), and this idea is “that idea which God hath of himself [and therefore] … absolutely himself.” And God the Father loves this perfect idea. And in short, God the Father eternally generates the Son by beholding his “most perfect idea of himself” (indeed, his beholding is his generating). And when he loves what he beholds, the love is a most perfect love—and God is love (John 4:8, 16). Therefore, the love that God the Father has for the Son is God—God the Holy Spirit. In short, the Holy Spirit is the act of the Father eternally begetting (beholding) the Son.
And from Edwards, I see a connection between his metaphor of “idea” and Augustine’s “intellect, memory, will” metaphor. Just as the Father generates the Son, so to understand is to generate memory (an “idea”). To have understanding is to have memory. To not have memory is to not understand. And therefore, the act of remembering (which, combined with understanding, is what makes a memory a memory) is the will (or love or volition or desire). In the same way, according to Edward’s trinitarian metaphysics, love is the very act of the Father beholding his “most perfect idea of himself.” Just as will is the act of understanding generating memory, so also love is the act of the Father generating the Son.
Our God Loves Community
Because our God is Trinity, humans desire community. This is partially what it means to bear the imago Dei (“image of God”). And so, whenever people (especially brothers and sisters) come my way, asserting their “God-given” right for autonomous, lone-wolf living, my response is a gentle reminder that they were created by a God who loves community because he himself is community, and that he loves his people to live in community—indeed, that’s what he created us for. Our culture boasts in individuality, and Christians should take heed of its influence. And I think an anthropology grounded in a robust doctrine of the Trinity is the unshakable ground on which to take heed.
 Saint Augustine, The Trinity, ed. John E. Rotelle, trans. Edmund Hill, 2nd ed. (New York: New City Press, 2015).
 Augustine's Latin Old Testament was based on the Septuagint, the Greek translation of the Hebrew Old Testament. Isa 7:9: ἐὰν μὴ πιστεύσητε, οὐδὲ μὴ συνῆτε (also Old Latin, which served as the basis for Augustine’s Bible: si non credideritis, neque intelligetis); Contra the Hebrew: אם לא תאמינו כי לא תאמנו (also Jerome’s Vulgate, which is based on the Hebrew: si non credideritis non permanebitis).
 See the following for Edwards citations: http://edwards.yale.edu/archive?path=aHR0cDovL2Vkd2FyZHMueWFsZS5lZHUvY2dpLWJpbi9uZXdwaGlsby9nZXRvYmplY3QucGw/Yy4yMDozLndqZW8=.