The chapter
Simply The whole chapter is one prayer, said out loud with the disciples listening. He prays first about himself and the work he has finished, then for the eleven who are with him, and then for everyone who will believe because of them. What he asks for them, more than once, is that they be one.
Context This is the longest prayer of Jesus recorded anywhere in the four Gospels in this app, and it is not a private one: it comes in the middle of a conversation, after 16:33 and before the crossing of the Kidron at 18:1, so the disciples hear every word of what is asked for them. It divides cleanly in three, at verses 1, 9 and 20, and the third division is the one that reaches past the room. Verse 20 prays for people who do not exist yet, named only as those who will believe through their word.
Verses 1-5
Simply He lifts his eyes and says the hour has come. He asks the Father to glorify him so that he can glorify the Father. He says eternal life is knowing the only true God and the one he sent, that he has finished the work he was given, and asks for the glory he had before the world existed.
Context Verse 3 is the only place in the four Gospels where eternal life is given a definition rather than a promise, and the definition is knowing rather than having. Verse 4 says the work is finished, in a prayer spoken before the arrest, which is worth setting beside the word he says from the cross at 19:30. The hour that has come here has been called not yet come three times earlier in the book, at 2:4, 7:30 and 8:20.
Verses 6-19
Simply He says he has made the Father's name known to the men given to him, and that they have kept the word. He prays for them and says plainly that he is not praying for the world at this point but for them. He asks that they be kept and be one, that they have his joy, and that they be kept from evil rather than taken out of the world, because he is sending them into it.
Context Verse 15 is the request most often reversed when it is remembered: he asks specifically that they NOT be taken out of the world, and verse 18 gives the reason, that they are being sent into it as he was. Verse 12 is the hardest line in the section and the file leaves it as it stands, with the one who is lost named only by a phrase. Verse 9's I do not pray for the world reads harshly on its own and is answered eleven verses later by a prayer whose stated purpose is that the world may believe.
Verses 20-26
Simply He says he is not praying only for these, but also for those who will believe in him through their word, and asks that they all be one, as the Father is in him and he in the Father, so that the world may believe. He asks that they be with him where he is and see his glory, and ends by saying he has made the Father's name known and will go on making it known.
Context The word one appears four times in verses 21 to 23, and each time it is tied to a purpose outside the group: that the world may believe, that the world may know. Unity is asked for as evidence rather than as comfort, which is a harder thing to pray for and a harder thing to be. Verse 24 shifts from asking to desiring, and it is the only request in the prayer that is about being somewhere rather than being kept from something.