"Men and brethren, sons of the family of Abraham, and those among you who fear God, to you the word of this salvation has been sent. For those who dwell in Jerusalem, and their rulers, because they did not know Him, nor even the voices of the Prophets which are read every Sabbath, have fulfilled them in condemning Him. And though they found no cause for death in Him, they asked Pilate that He should be put to death. Now when they had fulfilled all that was written concerning Him, they took Him down from the tree and laid Him in a tomb. But God raised Him from the dead. He was seen for many days by those who came up with Him from Galilee to Jerusalem, who are His witnesses to the people. And we declare to you glad tidings--that promise which was made to the fathers. God has fulfilled this for us their children, in that He has raised up Jesus. As it is also written in the second Psalm: 'You are My Son, today I have begotten You.' And that He raised Him from the dead, no more to return to corruption, He has spoken thus: 'I will give you the sure mercies of David.' Therefore He also says in another Psalm: 'You will not allow Your Holy One to see corruption.' For David, after he had served his own generation by the will of God, fell asleep, was buried with his fathers, and saw corruption; but He whom God raised up saw no corruption. Therefore, let it be known to you, brethren, that through this Man is preached to you the forgiveness of sins; and by Him everyone who believes is justified from all things from which you could not be justified by the law of Moses" (Acts 13:26-39).
Paul's teaching here is similar in many respects to Peter's sermons we have studied previously in the book of Acts (e.g., Acts 2 & 3). This fact should not surprise us since they both spoke by inspiration of the Holy Spirit; they both preached the same gospel message!
Paul's focus in this part of his sermon was upon the tragic mistakes that had been made by the Jewish people (particularly the religious leaders) toward Jesus of Nazareth. They did not really comprehend the messages from God of old that spoke prophetically of the coming Savior. Thus, they did not identify Jesus as the Messiah. He did not match their mistaken expectations of a ruler with great physical might. Rather than submitting to Him, they cast aside justice and labored to have Him killed (with the assistance of Pontius Pilate). Their wickedness was known before by God, however. Even in their sins they fulfilled Scripture (e.g., Psa. 22; Isa. 53)!
Jesus was buried but did not remain that way for long. On the third day (which was also the first day of the week), God raised Jesus from the dead, never more to die again! God reversed the unjust death sentence! He did not allow His "Holy One to see corruption"; in other words, He did not allow Jesus' body to rot in the grave. That particular prophecy could not have been referring to David, for his body did see corruption in the grave.
After Paul spoke of Jesus as the Christ, the sins of the people in slaying the innocent Son of God, and the resurrection of Christ, he is now ready to move his audience to action. There is something to be done with this information! These truths, when believed and obeyed, make salvation from sins possible (cf. Heb. 5:8,9)! Such justification was not fully possible strictly under the terms of the Mosaic dispensation (cf. Heb. 10:1-4). As we have seen elsewhere in the book of Acts, those who believed in Jesus, and what His sacrifice accomplished, repented of their sins, and were immersed in water for forgiveness (and were thus added to the church by the Lord) would be saved. This is the ultimate connection to the promise of old that was initially made to Abraham (cf. Gen. 12:1-3; 22:18). His Seed would yield a blessing for all the world. Jesus Christ, a descendant of Abraham, did bless all the world through His obedient life and sacrificial death by making salvation possible for all the world! He took the penalty of sin upon Himself and became the perfect atoning sacrifice. He was victorious over the devil and over death itself (cf. Heb. 2:14,15; I Cor. 15:54-57). Is there any greater blessing one can contemplate?