We also need to remember that the purpose of the Holy Spirit was not given primarily to empower the apostles to preach the Gospel of the Kingdom, but to also prove their Apostolic Authority (Mar 16:14-18).
VERSE 13: The God of Abraham, and of Isaac, and of Jacob, the God of our fathers, hath glorified his Son Jesus; whom ye delivered up, and denied him in the presence of Pilate, when he was determined to let him go. Notice that he is still addressing Israel and he is making his second point, which is that God has glorified his Son Jesus. It was not a good news message at all. Just bad news in that they were now guilty of killing their own long-awaited Messiah.
VERSES 14-15: But ye denied the Holy One and the Just, and desired a murderer to be granted unto you; And killed the Prince of life, whom God hath raised from the dead; whereof we are witnesses. The bad news continued. Not only had they denied the Holy One, but also desired a murderer to be granted to them instead. Not good. This happened in Mat 27:15-24. Peter goes on to say that now the one that they had killed, God hath raised from the dead, and not only they, but many others were eyewitnesses.
VERSE 16: And his name through faith in his name hath made this man strong, whom ye see and know: yea, the faith which is by him hath given him this perfect soundness in the presence of you all. This is the first time that faith is mentioned in the book of Acts, but it has nothing to do with a saving faith. It was only a faith in his name that this man was healed. We will not see saving faith until we get to Acts 13 when Paul is addressing the people in Antioch where they were first called Christians. Also, please understand that there is no church doctrine to be found in the book up to this point because there is no Body of Christ at this point.