Paul gave an overview from old to new

Acts 13:15-32,34-38,40-41
[15]After the reading from the Law of Moses and from the writings of the prophets, the officials of the synagogue sent them a message: “Brothers and sisters, we want you to speak to the people if you have a message of encouragement for them.”
[16]Paul stood up, motioned with his hand, and began to speak:“Fellow-Israelites and all Gentiles here who worship God: hear me!
[17]The God of the people of Israel chose our ancestors and made the people a great nation during the time they lived as foreigners in Egypt. God brought them out of Egypt by his great power,
[18]and for forty years he endured them in the desert.
[19]He destroyed seven nations in the land of Canaan and made his people the owners of the land.
[20]All this took about 450 years.“After this he gave them judges until the time of the prophet Samuel.
[21]And when they asked for a king, God gave them Saul son of Kish from the tribe of Benjamin, to be their king for forty years.
[22]After removing him, God made David their king. This is what God said about him: ‘I have found that David son of Jesse is the kind of man I like, a man who will do all I want him to do.’
[23]It was Jesus, a descendant of David, whom God made the Saviour of the people of Israel, as he had promised.
[24]Before Jesus began his work, John preached to all the people of Israel that they should turn from their sins and be baptized.
[25]And as John was about to finish his mission, he said to the people, ‘Who do you think I am? I am not the one you are waiting for. But listen! He is coming after me, and I am not good enough to take his sandals off his feet.’
[26]“My fellow-Israelites, descendants of Abraham, and all Gentiles here who worship God: it is to us that this message of salvation has been sent!
[27]For the people who live in Jerusalem and their leaders did not know that he is the Saviour, nor did they understand the words of the prophets that are read every Sabbath. Yet they made the prophets’ words come true by condemning Jesus.
[28]And even though they could find no reason to pass the death sentence on him, they asked Pilate to have him put to death.
[29]And after they had done everything that the Scriptures say about him, they took him down from the cross and placed him in a tomb.
[30]But God raised him from death,
[31]and for many days he appeared to those who had travelled with him from Galilee to Jerusalem. They are now witnesses for him to the people of Israel.
32 And we are here to bring the Good News to you: what God promised our ancestors he would do, he has now done for us, who are their descendants, by raising Jesus to life. As it is written in the second Psalm: ‘You are my Son;     today I have become your Father.’
[34]And this is what God said about raising him from death, never to rot away in the grave: ‘I will give you the sacred and sure blessings     that I promised to David.’
[35]As indeed he says in another passage: ‘You will not allow your faithful servant to rot in the grave.’
[36]For David served God’s purposes in his own time, and then he died, was buried with his ancestors, and his body rotted in the grave.
[37]But this did not happen to the one whom God raised from death.
38 We want you to know, my fellow-Israelites, that it is through Jesus that the message about forgiveness of sins is preached to you; and that everyone who believes in him is set free from all the sins from which the Law of Moses could not set you free.
[40]Take care, then, so that what the prophets said may not happen to you:
[41]‘Look, you scoffers! Be astonished and die! For what I am doing today     is something that you will not believe,     even when someone explains it to you!’ ”