Concerning the prayer itself:
Bengel: This chapter, of all the chapters in Scripture, is the easiest in regard to the words, but the most profound in regard to the ideas meant. . . . He prays to the Father, and at the same time teaches His disciples.
Ylvisaker: He prays the prayer which David Chytraeus, the pupil of Melanchthon, has called the sacerdotal prayer.
Fahling: Spener, a devout preacher, never ventured to preach upon it because he believed that its true understanding exceeded the ordinary measure of faith; but he caused it to be read to him three times on the evening before he died.
Lenski: This prayer lies on a plane that is so exalted that no disciples can join in its utterance. . . . The simple address 'Father' repeated in 5, 21 and 24, is peculiarly fitting for the Son in the sense in which Jesus differentiates 'my Father' from 'your father' in John 20: 17.
John 13:31-16:33, which was addressed entirely to the disciples. The entire chapter is addressed to His Father. "The hour has come." Previously (7:30; 8:20) He had said that His hour had not come. This "hour" covers His suffering, death, resurrection and ascension.
"Glorify" refers to Jesus' humanity because only the humanity could be clothed in splendor. "Son" refers to His divinity. Cf. John 1:14; Acts 3:15; 1 Corinthians 2:8; Galatians 4:4; 1 Timothy 3:16 where both natures are stressed.
Jesus prays for the mutual glorification of Son and Father. The Son could do so only because the Father glorified the Son. How this was to be done is explained in the next verse.
"Him" denotes the human nature. Look at Matthew 28:18. The Father gave the human nature of Jesus power and authority over the entire universe. Look at Luke 10:22.
The Father gave to the Son and in turn the Son gave. Forms of "give" occur seventeen times in this chapter. Nowhere else with such frequency. In thirteen instances it denotes what the Father gave to the incarnate Christ. And in the remaining four it denotes what Christ gave to man. The Father gave me to the Son and the Son gives and gives to me. Synergism is excluded.
This verse does not teach a limited atonement as say the Reformed. He is stressing and praying for the believers. That is not a limited atonement. What is Jesus' gift to me? Life eternal.
The verse introduces a noun clause which defines eternal life not as to what we will experience after death but in terms of knowledge already now. Here "know" denotes the revealed, intimate, saving knowledge."The only genuine God." The pagans had a multiplicity of gods and could not say "only." The unbelieving Jews rejected Christ and, therefore, did not have the "genuine" God. Therefore Jesus adds "and" because the only, the genuine God cannot be known apart from Jesus Christ. As Bengel points out, Jesus is not saying that He Himself and the Holy Spirit are not God. Jesus did not come on His own. He was sent with a commission by the Father .
Jesus first glorified the Father. Now He asks the Father to glorify Him. Note juxtaposition of pronouns again. In verse 5 it was "I you" now it is "Me you." He addresses the Father in a sense that He alone can address Him. No mere man could ever say this.
Jesus is speaking as the incarnate Christ in the state of exaltation. The human nature now will fully use all the qualities of the divine nature.
"I was constantly having." This includes both the preincarnate state and the state of humiliation. The Kenoticists apply it only to the preincarnate and the Arians apply it to neither, for they deny the divinity of Jesus.
The whole point is that God is asked to glorify Jesus by glorifying His human nature with the divine glory had from eternity and had also in the state of humiliation.
In verses 1-5 He speaks about the mutual glorification of Father and Son. He uses the verb "glorify" four times. Jesus' work, His suffering, death, resurrection and ascension, glorify the Father, glorify the Son, and give all benefit to a world lost in sin. In verses 1-3 Jesus speaks of Himself in the third person. He refers to Himself as the Son and as Jesus Christ. In verses 4-5 Jesus speaks about people and prays in their behalf.
He begins with the word "I have made plain." It reminds us of John 1:18. It is clear that Jesus is speaking about the elect, but this verse by no means says that the atonement is limited. People become Christians only because the Father gives them to Jesus. Synergism is eliminated.
They were the Father's, by His grace and mercy. This is the Christian's great comfort. The Christian is the Father's gift to Christ.
"And your Word they have kept." Jesus has the disciples in mind, but it applies likewise to all Christians. Note that throughout this prayer the sins of the disciples and of Christians are not mentioned. Had the disciples consistently kept the Father's Word? They had sinned often, but Jesus does not mention that. He constantly forgives them.
"Now, in view of the situation."  "Know" denotes intimate, saving knowledge. Look at John 10:14. A Christian knows and believes that he became a Christian only because the Father gave him to Jesus. The Christian did not make a decision or a commitment to become a Christian. He could not do that. All is a gift.
The reason for the knowledge in verse 7 is now plainly stated. The utterances which Jesus spoke are nothing more nor less than what the Father gave Jesus. He gave it to men. Their reaction is denoted by three aorist verbs. They received, came to know, came to believe. Christians receive the Word of Jesus as the very Word of the Father. Christians know that this God-man came from the Father. Christians believe that the Father sent the Son with a commission.
"For" means not only "concerning" but also "in behalf of." This was for the disciples in the first instance but also all Christians by extension. That becomes clear in the next sentence.
The divinity of Jesus is implicit here. The remainder of this verse does not mean that the atonement is limited, as say the Reformed. Here He speaks of the special high priestly intercession for believers. Look at Hebrews 7:25; 9:24; 1 John 2:1; Romans 8:34. Isaiah 53:12 and Luke 24:34 clearly show that Jesus prayed for all. He laid God's anger by in the atonement.
Here He prays for those who know and believe that the Father gave them to the Son as a gift. These are very simple words, but they are profound. Do we really believe that Jesus prays for us? Do we really believe that we became Christians only because the Father gave us to Jesus as a gift? These are soul-searching questions.
"And the mine all yours are and the yours mine." Only God could say this. Jesus is true God. By the way, I belong to the Father and the Son. Nothing can take me from Them.
"I have been and still am glorified." Not an easy prepositional phrase. It means in their redemption and what has resulted from it. Not only does the Father glorify His Son by the death, resurrection and ascension, but the objects of redemption glorify Jesus. My justification and sanctification glorify Jesus. It reminds one of Matthew 5:16. The Atonement was by no means fruitless.
The first clause speaks as if Jesus had already been glorified. His former relationship to people is now nearly over. The second phrase says "and yet." This applies to the disciples but to me also.
By the way, "world" occurs with unparalleled frequency in this chapter, eighteen times. In both instances in verse 11 it means "the world of human beings." In the first instance it means that Jesus' state and relationship to people is undergoing a change. In the second instance it means that they are left alone in the world, and yet not alone.
"To you come," denotes Jesus, the Highpriest. How will they manage, left in a sinful world of people?
Here the Father is addressed as "Holy Father." (By the way, what arrogance that the Pope has assumed this title to himself!) Who alone can preserve and keep Christians in a sinful world? The Holy Father. He is holy in Himself and cannot err.
"Keep" in the sense of "preserve."
His name which is His revelation. That is His Word. The Father gave that revealing Word to the Son for a purpose. Christians are a unity just as Father and Son are one in essence. Bengel says that the unity in essence between Father and Son is by nature but the unity among Christians is by grace. The two unities are not identical but analogous. Christians do not create unity. They merely discover in each other what the Father, through Christ, has caused by the Word.