Luke's fascinating story takes a significant turn (for the better!) in these chapters of Acts. Saul (later, "Paul") converts, not from Judaism to "Christianity" but from being a persecutor of Jesus followers (now called people of "The Way") to becoming a disciple of Jesus (9.1-19). He begins preaching about Jesus, is treated with suspicion, is threatened by his Jewish co-religionists and is whisked away, secreted out of Damascus, back to his hometown of Tarsus (9.20-30). Peter next returns to Luke's story. He heals in towns away of Jerusalem and closer to the Mediterranean (9.32-43), lodges with an unclean tanner where he has a perplexing vision, and then to Caesarea into the household of a Gentile. He is convinced that God's Spirit is at work among these Gentile Romans and baptises the household. This is a major turning point in Luke's story  (10.1-48). Through Peter's action, Gentiles are now incorporated into the Jesus movement, originally Jewish. Peter later explains his actions to the Jerusalem leadership (11.1-18) who declare "To the Gentiles also God has granted repentance until life" (11.18). 

Notes (from the Catholic Parish of Lockleys in South Australia--www.lockleysparish.com) that accompanies this presentation can be found here.