Jesus continues teaching among the Jews, though the leaders are against Him and the people divided in their opinion about Him. Jesus says He is living water that the people pray to God for. The one charge against Him they have (healing on the Sabbath) is a bogus charge. Their other objection (He is from Galilee) is based on a false understanding (He WAS born in Bethlehem, and is of David).
They try to drum up another charge, since they know He is right on the first one, above. Jesus makes a stunning statement without words by writing their names in the dust. Please read Jeremiah 17:13 to see what He says: they have forsaken Yahweh, the fountain of living water, which Jesus claimed to be half a chapter earlier. And the critics don't think this text is Scripture.
Jesus deals gently with the woman caught in adultery, as Joseph did with Mary, in what he thought was a similar situation.
Jesus' authority and witness is His Father. The Jews who reject Jesus don't know His Father, so can't believe Him. While some believe, Jesus gets more forceful with those who don't. They are slaves in God's house, refusing to be set free by the Son. Though they are in God's house as children of Abraham (by circumcision), their spiritual father is the devil. Jesus asserts His authority even over death, saying that anyone who believes and follows Him, He won't let die. The Jews take this as blasphemy, ruling out the possibility He is telling the truth.