Here are some thoughts on St Matthew's version of the Lord's Prayer, many taken from or loosely inspired by things people said at our Department Bible study yesterday (though what I say should not be taken as representing anything like a consensus). First, my translation:
9Our father, who art in heaven:
Thy name be sanctified,
10thy kingdom come,
thy will come to pass,
as in heaven so on earth.
11Give us daily our supersubstantial [epiousion] bread.
12And forgive us our debts
as we forgive our debtors.
13Do not bring us to a trial,
but instead deliver us from the evil one [tou ponerou]. (Matthew 6:9-13)
The overall theme is that of the earthly and the heavenly, with the earthly being brought in conformity with the heavenly, by our own activity and that of our father. "As in heaven so on earth", I take it, applies to each: "thy name be sanctified", "thy kingdom come" and "thy will come to pass." Each of these three is simultaneously a request and a personal commitment to the indicated task, and in each case the act of praying is already partly constitutive of the prayed-for result: by praying these we sanctify our Father's name, make his kingdom present and do his will.
Implicit behind all three requests is an image of the majesty of God enthroned above the heavenly hosts who sanctify his name and bring his will to pass--and yet this King of the Universe is also our father.
The prayer is enveloped between the "father" (the first word in the Greek--while in Aramaic and Hebrew, "our father" would be one word) and "the evil one" at the end. This involves reading tou ponerou as "the evil one" (masculine) rather than as generically "evil" (neuter). This is supported the neatness of the resulting envelope structure, the central focus in the prayer on the beyond-earthly significance of our actions, as well as the implicit imagery of the angels of the heavenly host.
The central request is for our epiousios bread. We really don't know how to translate the word. A leading view is that it is the bread for the day to come. But it could also be the bread needed for our existence or ousia, the bread for the life to come, or, following St Jerome's Latin calque, the supersubstantial bread. In any case, the Church has traditionally taken a Eucharistic reading of the text, and such a reading makes the tendency of the earthly towards the heavens come to a head here: we sanctify his name and do his will just as the angels do, and here we boldly ask for the bread of angels, the new manna, the earthly bread made into the body of him who became flesh for us, the bread that is literally the Logos of God on which man lives (cf. Jesus' struggles with the evil one two chapters back in Matthew). At the same time, this reading should not rule out--and indeed the heavenly-earthly parallelism structure is very friendly to it--that this is also a request for what we need for our earthly lives from our heavenly royal father.
In verse 12, we have a switch from the positive to the negative aspects of transforming the earthly into the heavenly. The debt of our sin to God imposes on us an obligation we cannot pay and yet paying which is essential to the coming of his kingdom on earth. We boldly ask that it be forgiven, because (seemingly a non sequitur, but yet God in love for our children makes it follow) of our forgiving the debts of our debtors. It is neither good to be debtor nor creditor, and here by ceasing to be creditors we cease to be debtors. The forgiveness here is in the first instance a loosing or a release. The essential effect is normative, that the debtor is quit of the debt. Of course, when we forgive another, the essential effect is not all that we are called to: we are called to an affective component--we should feel as if the person who sinned against us is no longer in debt to us--and sometimes to a concrete reaching out to heal the relationship. Likewise, God's forgiveness heals us, and gives us the grace to avoid incurring further indebtedness, as indicated by the next verse.
The trials of verse 13 may well include ordinary temptations, but it is also plausible that the text is specifically talking of the trials of persecution and torture. We pray that our father not bring us there, and at the same time we should not deliberately take ourselves there either (there is the scary story in Eusebius about the early Christian who from bravado turned himself in to the Romans--and then broke down and apostasized). Finally, we are reminded that we do not struggle against mere flesh and blood, but that persecutions and temptations are the work of infernal intelligence, like the devil that Jesus fought two chapters back.