Anselm (1033-1109) was Archbishop of Canterbury and wrote many influential works, including his Proslogium, Monologium and Cur Deus Homo. He is most famous for his Ontological Argument, which is one of the most famous proofs for the existence of God (in Proslogium), as well as for his argument for Satisfaction Atonement (in Cur Deus Homo trans. "Why God Became a Man").
I'm reading through Oxford World Classic's book: Anselm of Canterbury: The Major Works. After a short biography of Anselm, is Anselm's first major work: Monologium (online text). Monologium reads as Philosophy book with many Aristotelian Syllogisms. Monologium introduces Anselm's Ontological Argument (which is presented in its fullness in his subsequent Proslogium.)
Anselm's use of Antithesis is what makes his arguments so persuasive. The following is an example from Monologium where Anselm discusses the three ways that the following statement could be interpreted: "How it is to be understood that this Nature created all things from nothing?"
What, then, is to be our understanding of the term nothing?—For I have already determined not to neglect in this meditation any possible objection, even if it be almost foolish.—In three ways, then—and this suffices for the removal of the present obstacle—can the statement that any substance was created from nothing be explained.
There is one way, according to which we wish it to be understood, that what is said to have been created from nothing has not been created at all; just  as, to one who asks regarding a dumb man, of what he speaks, the answer is given, “of nothing,” that is, he does not speak at all. According to this interpretation, to one who enquires regarding the supreme Being, or regarding what never has existed and does not exist at all, as to whence it was created, the answer, “from nothing” may properly be given; that is, it never was created. But this answer is unintelligible in the case of any of those things that actually were created.
There is another interpretation which is, indeed, capable of supposition, but cannot be true; namely, that if anything is said to have been created from nothing, it was created from nothing itself (de nihilo ipso), that is, from what does not exist at all, as if this very nothing were some existent being, from which something could be created. But, since this is always false, as often as it is assumed an irreconcilable contradiction follows.
There is a third interpretation, according to which a thing is said to have been created from nothing, when we understand that it was indeed created, but that there is not anything whence it was created. Apparently it is said with a like meaning, when a man is afflicted without cause, that he is afflicted “over nothing.”
-- Anselm, Monologium Chapter VIII
The Ontological Argument
The word "Ontological" is derived from the Latin words "Ont" and "Logia" that mean the reason of being or the logic of being. Although the Ontological Argument is most clearly defined in Proslogium, there are three works by Anselm that should be read together to fully understand the Ontological Argument and Anselm's answers to objections: Monologium, Proslogium, and Reply to Gaunilo. The last work, Reply to Gaunilo, answers objections raised to the Ontological Argument in a short letter titled Pro Insipiente (On behalf of the Fool) by Gaunilo of Marmoutiers.
The Ontological Argument is as Anselm wrote "we believe that thou art a being than which nothing greater can be conceived." Or in other words that there is a being which is greater than all beings, or rather there necessarily is a being in which nothing greater could be conceived, and the argument is even extended that there must be a being greater than what may be conceived. So therefore this being must be God. Here is the argument is Anselm's own words:
Ontological Argument in Proslogium:
CHAPTER II. Truly there is a God, although the fool hath said in his heart, There is no God.
AND so, Lord, do thou, who dost give understanding to faith, give me, so far as thou knowest it to be profitable, to understand that thou art as we believe; and that thou art that which we believe. And indeed, we believe that thou art a being than which nothing greater can be conceived. Or is there no such nature, since the fool hath said in his heart, there is no God? (Psalms xiv. 1). But, at any rate, this very fool, when he hears of this being of which I speak—a being than which nothing greater can be conceived—understands what he hears, and what he understands is in his understanding; although he does not understand it to exist.
For, it is one thing for an object to be in the understanding, and another to understand that the object exists. When a painter first conceives of what he will afterwards perform, he has it in his understanding, but he does not yet understand it to be, because he has not yet performed it. But after he has made the painting, he both has it in his understanding, and he understands that it exists, because he has made it.  Hence, even the fool is convinced that something exists in the understanding, at least, than which nothing greater can be conceived. For, when he hears of this, he understands it. And whatever is understood, exists in the understanding. And assuredly that, than which nothing greater can be conceived, cannot exist in the understanding alone. For, suppose it exists in the understanding alone: then it can be conceived to exist in reality; which is greater.
Therefore, if that, than which nothing greater can be conceived, exists in the understanding alone, the very being, than which nothing greater can be conceived, is one, than which a greater can be conceived. But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.
CHAPTER III. God cannot be conceived not to exist.—God is that, than which nothing greater can be conceived.—That which can be conceived not to exist is not God.
AND it assuredly exists so truly, that it cannot be conceived not to exist. For, it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that, than which nothing greater can be conceived. But this is an irreconcilable contradiction. There is, then, so truly a being than which nothing greater can be conceived to exist, that it cannot even  be conceived not to exist; and this being thou art, O Lord, our God.
So truly, therefore, dost thou exist, O Lord, my God, that thou canst not be conceived not to exist; and rightly. For, if a mind could conceive of a being better than thee, the creature would rise above the Creator; and this is most absurd. And, indeed, whatever else there is, except thee alone, can be conceived not to exist. To thee alone, therefore, it belongs to exist more truly than all other beings, and hence in a higher degree than all others. For, whatever else exists does not exist so truly, and hence in a less degree it belongs to it to exist. Why, then, has the fool said in his heart, there is no God (Psalms xiv. 1), since it is so evident, to a rational mind, that thou dost exist in the highest degree of all? Why, except that he is dull and a fool?
-- Anselm, Proslogium, Chapters II-III
Reply to Gaunilo's Lost Island counterexample to the Ontological Argument
In Anselm's Reply to Gaunilo, he answers many objections to the Ontological Argument that helps clarify what was already said in the Monlogium and Proslogium. This work contains an analogy to a "Lost Island" that is a utopia, greater than all other islands, and it has perfect fertility, etc. And Gaunilo used this Lost Island as a greatest island of which may though but considered it a counter argument because it may not exist and he had a right to doubt its existence. Anselm, via Anthesis explains that the Lost Island is not a necessary being, because it could not exist and yet all other islands may still exist. The greatest being in the Ontological Argument is a necessary being, where the Lost Island is not a necessary being.
Reply to Gaunilo, CHAPTER III. A criticism of Gaunilon’s example, in which he tries to show that in this way the real existence of a lost island might be inferred from the fact of its being conceived.
BUT, you say, it is as if one should suppose an island in the ocean, which surpasses all lands in its fertility, and which, because of the difficulty, or the impossibility, of discovering what does not exist, is called a lost island; and should say that there can no doubt that this island truly exists in reality, for this reason, that one who hears it described easily understands what he hears.
Now I promise confidently that if any man shall devise anything existing either in reality or in concept alone (except that than which a greater be conceived) to which he can adapt the sequence of my reasoning, I will discover that thing, and will give him his lost island, not to be lost again.
But it now appears that this being than which a greater is inconceivable cannot be conceived not to  be, because it exists on so assured a ground of truth; for otherwise it would not exist at all.
Hence, if any one says that he conceives this being not to exist, I say that at the time when he conceives of this either he conceives of a being than which a greater is inconceivable, or he does not conceive at all. If he does not conceive, he does not conceive of the non-existence of that of which he does not conceive. But if he does conceive, he certainly conceives of a being which cannot be even conceived not to exist. For if it could be conceived not to exist, it could be conceived to have a beginning and an end. But this is impossible.
He, then, who conceives of this being conceives of a being which cannot be even conceived not to exist; but he who conceives of this being does not conceive that it does not exist; else he conceives what is inconceivable. The non-existence, then, of that than which a greater cannot be conceived is inconceivable.
-- Anselm, Reply to Gaunilo, Chapter III.
Jonathan Edward's Unpublished Essay on the Trinity verses Anselm's Monologium
The Monologium is strikingly similar to Jonathan Edward's Discourse on the Trinity (mirror) (also known as Edward's "Unpublished Essay on the Trinity) that's in Yale's Vol 21 of WJE Online Words of Edwards. The Monologium is a proof for the Trinity based on the concepts underlying the Ontological Argument. After discussing the Greatest Being, then he consider that's being's Wisdom as the begotten Son, and that the Holy Spirit is breated-out (spirated) and not begotten from the unbegotten and begotten deities to form one being in three persons. At the very end he puts the names Father, Son and Holy Spirit on to each of the three descriptions.
Anselm defines a being that which is the greatest of what may be thought, and then considers that being. The Monologium uses concepts similar to Plato's forms or Aristotle's Categories to discuss the perfection of Wisdom and Justice. Anselm proves God's Simplicity by stating that God will be the sum of all attributes in their greatest form that will result in a being without division. He also discusses since all things are derived from God then God is everywhere, because otherwise there would be an existing being that is not derived from God. So therefore God is all places, and he also shows that God is at all times, and consequently God could not be at one particular place because that would mean there would be other places where God was not. This is why God's nature must necessarily be different than created nature.
Edward's uses Lockean Idealism to do the same thing, starting with God's idea of Himself, and then the Love of that Idea. I found that the Monologium is supported in the same way through the nature of greatest being. Edwards uses copious scriptures to support his proof where Anselm does not provide scriptures or quotations from theologians. Anselm's argument for Simplicity adds something lacking from Edwards, because without closely thinking, Edward's essay at first could produce a pantheon of God via infinite recursion of God's Idea of the Idea of the Idea of Himself, ad infinitum, whereas the recursion in Anselm points to God's Simplicity and to a Perfection of Being, and would in Edwards case yield a perfection of Idealism. This is certainly not lacking from Edwards, but Anselm has made it clearer to me.
Anselm's Ontological Argument stood unopposed until Immanuel Kant's objections almost a thousand years later, and in fact it is still a very strong argument today (with many modified forms).
Related: Anselm, Anselm of Canterbury, Archbishop, cur deus homo, Discourse on the Trinity, Divine Simplicity, Immanuel Kant, Jonathan Edwards, Monologium, Ontological Argument, Pro Insipiente (On behalf of the Fool), Proslogium, Reply to Gaunilo, trinity, Unpublished Essay on the Trinity, Why God Became A Man