Luke 9 marks the shift of focus in Jesus ministry. Jesus has been in mission and ministry in and around the sea of Galilee with occasional forays up to Sidon and over into the Decapolis. In Chapter 9 the intensity of his ministry steps up. It begins with the mission of the 12 -- traveling, preaching, sharing the good news of the Kingdom of God -- this multiplies the message and influence. We find the feeding of the 5000 and the 12 baskets of fragments (10-17) -- which spreads his fame and reputation on a while new level. The key to the early part of 9 is to notice what happens after Peter's declaration (18-20) that he knows that Jesus is the Messiah (Christ). As soon as Peter confesses that he gets who Jesus really is, Jesus predicts his death and resurrection (an idea that the disciples do not understand until after the events).
In 28 we have the transfiguration -- so, after the revelation that Jesus is the Messiah by Jesus' followers he is revealed in a whole new way. Jesus is "transfigured" who he is on the inside is reveled on the outside. Notice that this is not a public event but is only seen by the inner leadership circle: Peter, James and John. Jesus in his changed state is joined by Moses and Elijah (the Law and the Prophets). It is the first time that any of the original 12 are allowed to see Jesus in his fullness and proper relationship to the spiritual history of the world.
Verse 51 of chapter 9 is the pivot of the Gospel. "When the days drew near for him to be taken up, he set his face to go to Jerusalem." I have often pondered what this must have been like. Jesus knew (he has said on two occasions in chapter 9) that when he gets to Jerusalem he will be betrayed, crucified and buried and after three days rise again. I cannot imagine what it had to have been like to face his purpose and destiny and all of its anguish and pain and horror with such resolute determination. How often it is vital for us to set our faces to the struggle and difficulty necessary to become all that God has called us to become.