This passage occurs in both the Narrative and Revised Common Lectionaries. The Revised Common Lectionary breaks it up into two separate passages; the narrative leaves it as one.
Summary: I don't know if one truly can summarize John 3. It is the chapter of all chapters in Scripture. The Greek shows a number of interesting wrinkles in the text, each of which can help get at the core message about the work of God, Father, Son and Holy Spirit, in saving the world. Perhaps one little tidbit: eternal life doesn't begin after death in the Gospel of John.
Νικόδημος ("Nicodemus" vs 1): It is worth noting that Nicodemus gets a name; the woman at the well in chapter 4 will not. Nicodemus, like the woman at the well, misunderstands Jesus. His story should end in chapter 3, but it does not. It keeps going. Because God is author of our story, our own failures do not end the narrative. In chapter 7 Nicodemus will defend Jesus; at the end of the Gospel he will help bury Jesus (19). Jesus invites people to come and see. For Nicodemus, this invitation changed his life, as he came and saw, and was drawn in.
Little side note: Nicodemus' general confusion is emphasized in the Greek that he repeated says "How can it be that..."
ο διδασκαλος ("the teacher", vs 2) Nicodemus calls Jesus "a" teacher; Jesus calls Nicodemus "THE teacher." Obviously Jesus is catching Nicodemus in his words!
ανωθεν ("again" or "above" vs 3) 'Above' is better here. Not simply because of the context (Jesus says you don't have to come out of the womb, but be born of the water and Spirit), but because above includes again. If you are born from above, this is the second birth anyway! We must be born again, but this birth isn't through human agency, but God alone.
πνευμα ("spirit" vs 5, 6 and 8) The word Spirit is related to breath (see: pneumatic in the word!), but also blow and wind. So the verse that reads "The wind blows where it will" means "the Spirit blows where it will." In fact, one could read it as "The spirit spirits where it will."
πιστευω ("believe" vs 15 and 16, etc). Believe is only a verb in the Gospel of John. It means trust; it is an action not a thing. It is also in the present and active tense: the one is who is trusting...
εχη ("have" vs 16) The word here is in the present tense. ETERNAL LIFE begins NOW. It is not a future reality, but a present one found in Christ! Whoever is trusting in God has life which continues into eternity.
κοσμος ("world" vs 16). Throughout the Gospel of John, the world doesn't like God. It doesn't understand God (1:10); it doesn't give like God (14:27) ; in fact, it hates God (7:7). This is the world God loves!