A lot of good points in the above post.
I just wanted to expand on what Tis_Bearself posted.
The distinction in the words used for love shows us that Jesus is desiring a complete and heroic love from Peter, but Jesus shows that He is willing, at the end of the conversation, to settle, at this time, for Peter’s friendship.
I really like verse 18 though, it sums up the story nicely. When ever I read Jesus saying Truly, truly (Amen, amen) I slow down and concentrate, because those are the words Jesus used when He is say PAY ATTENTION!
18 Truly, truly, I say to you, when you were young, you girded yourself and walked where you would; but when you are old, you will stretch out your hands, and another will gird you and carry you where you do not wish to go.”
Jesus is telling Peter here, you might have denied me three times. I’m going away now and you might not think you are capable of feeding and tending my flock. And at this time you might not believe you are capable of heroic love. However, I have faith in you and I am entrusting you with my flock because by the end I know you will love me with all you heart and be willing to lay down your life and never deny me again.
Deep, deep stuff in John’s Gospel is my favorite of the 4 gospels.