Following the Gospels, this book answers the question, “What’s next?” Since Jesus has ascended into heaven, the apostles are to go from Jerusalem, to Judea and Samaria, and to the ends of the earth. That’s what happens in this book. In chapters 1-7, they are in Jerusalem. Persecution pushes them out to Judea and Samaria (ch. 8-10). Finally, in chapter 13, the gospel starts to go to all the nations through the ministry of Paul.
One way to divide the book is to recognize that the first half (chs. 1-12) is mostly focused around the ministry of Peter. The second half (chs. 13-28) is centered around Paul. Paul takes three missionary journeys. Most of what he says and does is not recorded. Entire years are skipped over in a verse. But the main point that Luke makes is that nothing can stop the gospel from spreading to the ends of the earth. Not even a shipwreck!
Pay attention to the pattern of Paul’s ministry. He goes first to Jews (in the synagogue), and then when they reject him, he goes to the Gentiles. Note the consistent rejection of the Jews. Note also that Paul never gives up on them, and he always goes to them first wherever he is.