Objection 1. It seems that God is not one. For it is written "For there be many gods and many lords" (1 Corinthians 8:5).
Objection 2. Further, "One," as the principle of number, cannot be predicated of God, since quantity is not predicated of God; likewise, neither can "one" which is convertible with "being" be predicated of God, because it imports privation, and every privation is an imperfection, which cannot apply to God. Therefore God is not one.
On the contrary, It is written "Hear, O Israel, the Lord our God is one Lord" (Deuteronomy 6:4).
I answer that, It can be shown from these three sources that God is one.
First from His simplicity. For it is manifest that the reason why any singular thing is "this particular thing" is because it cannot be communicated to many: since that whereby Socrates is a man, can be communicated to many; whereas, what makes him this particular man, is only communicable to one. Therefore, if Socrates were a man by what makes him to be this particular man, as there cannot be many Socrates, so there could not in that way be many men. Now this belongs to God alone; for God Himself is His own nature, as was shown above (Question 3, Article 3). Therefore, in the very same way God is God, and He is this God. Impossible is it therefore that many Gods should exist.
Secondly, this is proved from the infinity of His perfection. For it was shown above (Question 4, Article 2) that God comprehends in Himself the whole perfection of being. If then many gods existed, they would necessarily differ from each other. Something therefore would belong to one which did not belong to another. And if this were a privation, one of them would not be absolutely perfect; but if a perfection, one of them would be without it. So it is impossible for many gods to exist. Hence also the ancient philosophers, constrained as it were by truth, when they asserted an infinite principle, asserted likewise that there was only one such principle.
Thirdly, this is shown from the unity of the world. For all things that exist are seen to be ordered to each other since some serve others. But things that are diverse do not harmonize in the same order, unless they are ordered thereto by one. For many are reduced into one order by one better than by many: because one is the "per se" cause of one, and many are only the accidental cause of one, inasmuch as they are in some way one. Since therefore what is first is most perfect, and is so "per se" and not accidentally, it must be that the first which reduces all into one order should be only one. And this one is God.
Reply to Objection 1. Gods are called many by the error of some who worshipped many deities, thinking as they did that the planets and other stars were gods, and also the separate parts of the world. Hence the Apostle adds: "Our God is one," etc.
Reply to Objection 2. "One" which is the principle of number is not predicated of God, but only of material things. For "one" the principle of number belongs to the "genus" of mathematics, which are material in being, and abstracted from matter only in idea. But "one" which is convertible with being is a metaphysical entity and does not depend on matter in its being. And although in God there is no privation, still, according to the mode of our apprehension, He is known to us by way only of privation and remotion. Thus there is no reason why a certain kind of privation should not be predicated of God; for instance, that He is incorporeal and infinite; and in the same way it is said of God that He is one.
Source: Summa Theologica (New Advent)