Acts begins with the same introduction as Luke; it was written to Theophilus as a second volume. It seems surprising that the other gospel writers did not seek to write a continuation as well. Perhaps they were forced to flee Jerusalem during the purges and did not have the ability to do further research to write an Acts-like account. In chapter one the twelve apostles felt it necessary to replace Judas, the betrayer, and selected Matthias by drawing lots. Nothing more is mentioned about him so we don’t know what became of him (or many of the others).
In Acts two we learn two important pieces of information. First, “They sold property and possessions to give to anyone who had need” (2:45). This indicates the radical nature of what it meant to become a Christian as well as their desire to help those less fortunate (Cf. 4:34ff). It was fortunate in the practical sense as well because when Christians were forced to flee Jerusalem they didn’t have to worry about their property. Secondly, “Every day they continued to meet together in the temple courts” (v46; 3:1). This shows that in the early stages Christianity was not seen as a separate religion and they still met in the temple. This would change as more Gentiles believed because they could only enter the court of Gentiles, which was full of merchants selling stuff (hence Jesus’ cleansing).
In the later half of chapter three Peter preaches to the crowds and explains Jesus’ relation to the Old Testament. Luke is known as a Gentile, writing to Gentiles, but Acts primarily records the story of early Christianity as it relates to the Jewish people and then flows out to include the Gentiles. From Jerusalem to Judea to the ends of the earth.