CTS 10 tells the story of the salvation of a Gentile named Cornelius. There was a time when it was hard for Christ's disciples to accept that there could possibly be a legitimate extension of the gospel to those who were not the physical descendants of Abraham. Peter's reaction to this reality is central to the lesson.
God had been working on this man named Cornelius and had produced what we might consider to be an Old Testament brand of faith and repentance in Him. But since the death, burial, resurrection and ascension of Jesus, and since the impartation of the Holy Spirit at Pentecost, it is apparent that faith in the name (and work) of Jesus Christ alone was essential for regeneration. It is perhaps a moot point that God and Peter both gave Cornelius considerable credit for His previous devotion, because the fact remains that God sent Peter to Cornelius so that Cornelius could hear the gospel of Jesus Christ, receive the gift of the Holy Ghost and be baptized in the name of the Lord (Acts 10:43-44). Surely, there were lessons both for Peter and for Cornelius on that day, but even more so for the rest of the church, then and now. Peter's presentation of the gospel and the grounds of his acceptance of Cornelius are both wonderfully revealing.