We have a series of different theories about Luke's purpose in writing Acts:

Very often the purpose has been seen in connection with the presentation of Paul. This is legitimate since from Acts 9 onwards Paul is the central figure and seventeen chapters are devoted to him. Three issues must be taken into account in considering Luke's purpose: (1.) the strong Jewish character of Acts; (2.) the interpretation of the Scriptures, and (3.) the position of the law-observant apostle and missionary to the Jews, Paul. The Jewish life of the churches is described in a way that shows it to be self-evident for the readers; the same is true for the interpretation of the Scriptures, whose authority is taken for granted. Far more difficult is the presentation of Paul. Other figures of the church are seen as well known to the readers – Peter, the Twelve, James the brother of the Lord, Barnabas etc., – whereas Luke presents Paul in every detail and his life apologetically, as if he were previously unknown to his readers, but in a way acceptable to them.