The summary

This form of prayer consists, as I have said, of six petitions. The first three, it ought to be known, relate to the glory of God, without any regard to ourselves; and the remaining three relate to those things which are necessary for our salvation. As the law of God is divided into two tables, of which the former contains the duties of piety, and the latter the duties of charity
“As the Law of God is divided into two Tables, of which the first contains the things which we owe to God to honor his majesty: the second, what we owe to our neighbor according to charity.” so in prayer Christ enjoins us to consider and seek the glory of God, and, at the same time, permits us to consult our own interests. Let us therefore know, that we shall be in a state of mind for praying in a right manner, if we not only are in earnest about ourselves and our own advantage, but assign the first place to the glory of God: for it would be altogether preposterous to mind only what belongs to ourselves, and to disregard the kingdom of God, which is of far greater importance.
Our Father who art in heaven Whenever we engage in prayer, there are two things to be considered, both that we may have access to God, and that we may rely on Him with full and unshaken confidence: his fatherly love toward us, and his boundless power. Let us therefore entertain no doubt, that God is willing to receive us graciously, that he is ready to listen to our prayers, — in a word, that of Himself he is disposed to aid us. Father is the appellation given to him; and under this title Christ supplies us with sufficiently copious materials for confidence. But as it is only the half of our reliance that is founded on the goodness of God, in the next clause, who art in heaven, he gives us a lofty idea of the power of God. When the Scripture says, that God is in heaven, the meaning is, that all things are subject to his dominions, — that the world, and everything in it, is held by his hand, — that his power is everywhere diffused, — that all things are arranged by his providence. David says, “He that dwelleth in the heavens shall laugh at them,” (Psalm 2:4); and again, “Our God is in heaven: he hath done whatever he hath pleased,” (Psalm 115:3).
When God is said to be in heaven, we must not suppose that he dwells only there; but, on the contrary, must hold what is said in another passage, that “the heavens of heavens do not contain him,” (2 Chronicles 2:6). This mode of expression separates him from the rank of creatures, and reminds us that, when we think of him, we ought not to form any low or earthly conceptions: for he is higher than the whole world. We have now ascertained the design of Christ. In the commencement of the prayer, he desired his own people to rest their confidence on the goodness and power of God; because, unless our prayers are founded on faith, they will be of no advantage.