Luke covers a lot of territory in chapter three. He sets the stage with a date – about 29 or 30 A.D. He moves quickly in twenty verses from the beginning of John’s ministry to the end, but he tells us plainly the content of his teaching and in doing so, introduces us to a major theme in Luke’s writings: repentance.
Baptism was for the forgiveness of past sins. However you understand baptism to work, it effects forgiveness. There is no way around it. In the same verbal construction, Jesus will refer to his death as the “blood of the covenant” that is poured out “for the forgiveness of sins” (Matthew 26:28). Jesus’ blood was not poured out because forgiveness had already been given, or even as a sign that they had been forgiven, but so that forgiveness could come about. Likewise, the blood of Jesus did not forgive any more than baptism does, but it was because of the blood (and baptism) that God forgives.
But baptism is not the focus of John’s teaching (even though John commanded it and Jesus submitted to it. Repentance was the focus. Baptism does no heavenly good if the person being baptized doesn’t live a different life. What good is it to be forgiven if you continue to live as you always have? Luke will refer to repentance more than any other writer – including Paul. But at the end of the Bible, the theme will be raised again in a prominent way in the book of Revelation. There, the warning is given and, interestingly, it is given to Christians. They must repent. Judgement will not only separate the Christians from those without Christ, but will separate those Christians who live like Christ from those who do not.
Luke and Matthew both include a genealogy of Jesus, but they differ. The only way to reconcile them is to say that one is the genealogy of Mary and the other of Joseph. They cannot both be the genealogy of one parent. In one, Jesus is the descendant of David’s son Solomon. In the other, he is the descendant of David’s son Nathan. Matthew’s purpose is to show Jesus’ Jewish heritage (thus he begins with Abraham). Luke’s purpose is to show Jesus is the Son of God, another important theme in Luke/Acts.