Objection 1. It seems that God does not know things besides Himself. For all other things but God are outside of God. But Augustine says (Octog. Tri. Quaest. qu. xlvi) that "God does not behold anything out of Himself." Therefore He does not know things other than Himself.
Objection 2. Further, the object understood is the perfection of the one who understands. If therefore God understands other things besides Himself, something else will be the perfection of God, and will be nobler than He; which is impossible.
Objection 3. Further, the act of understanding is specified by the intelligible object, as is every other act from its own object. Hence the intellectual act is so much the nobler, the nobler the object understood. But God is His own intellectual act. If therefore God understands anything other than Himself, then God Himself is specified by something else than Himself; which cannot be. Therefore He does not understand things other than Himself.
On the contrary, It is written: "All things are naked and open to His eyes" (Hebrews 4:13).
I answer that, God necessarily knows things other than Himself. For it is manifest that He perfectly understands Himself; otherwise His existence would not be perfect, since His existence is His act of understanding. Now if anything is perfectly known, it follows of necessity that its power is perfectly known. But the power of anything can be perfectly known only by knowing to what its power extends. Since therefore the divine power extends to other things by the very fact that it is the first effective cause of all things, as is clear from the aforesaid (2, 3), God must necessarily know things other than Himself. And this appears still more plainly if we add that the every existence of the first effective cause--viz. God--is His own act of understanding. Hence whatever effects pre-exist in God, as in the first cause, must be in His act of understanding, and all things must be in Him according to an intelligible mode: for everything which is in another, is in it according to the mode of that in which it is.
Now in order to know how God knows things other than Himself, we must consider that a thing is known in two ways: in itself, and in another. A thing is known in itself when it is known by the proper species adequate to the knowable object; as when the eye sees a man through the image of a man. A thing is seen in another through the image of that which contains it; as when a part is seen in the whole by the image of the whole; or when a man is seen in a mirror by the image in the mirror, or by any other mode by which one thing is seen in another.
So we say that God sees Himself in Himself, because He sees Himself through His essence; and He sees other things not in themselves, but in Himself; inasmuch as His essence contains the similitude of things other than Himself.
Reply to Objection 1. The passage of Augustine in which it is said that God "sees nothing outside Himself" is not to be taken in such a way, as if God saw nothing outside Himself, but in the sense that what is outside Himself He does not see except in Himself, as above explained.
Reply to Objection 2. The object understood is a perfection of the one understanding not by its substance, but by its image, according to which it is in the intellect, as its form and perfection, as is said in De Anima iii. For "a stone is not in the soul, but its image." Now those things which are other than God are understood by God, inasmuch as the essence of God contains their images as above explained; hence it does not follow that there is any perfection in the divine intellect other than the divine essence.
Reply to Objection 3. The intellectual act is not specified by what is understood in another, but by the principal object understood in which other things are understood. For the intellectual act is specified by its object, inasmuch as the intelligible form is the principle of the intellectual operation: since every operation is specified by the form which is its principle of operation; as heating by heat. Hence the intellectual operation is specified by that intelligible form which makes the intellect in act. And this is the image of the principal thing understood, which in God is nothing but His own essence in which all images of things are comprehended. Hence it does not follow that the divine intellectual act, or rather God Himself, is specified by anything else than the divine essence itself.
Source: Summa Theologica (New Advent)