"The book of Acts (also called Acts of the Apostles) begins where the Gospel of Luke left off. Before ascending into heaven, Jesus commissions His disciples to be His witnesses from Jerusalem to the end of the Earth (Acts 1:8). In fulfillment of this command, and through the power of the Holy Spirit, the early church expands. Acts shows what it means to be part of Jesus’ mission to the world. The apostles set the example of what it means to be fully devoted to Christ and enveloped by the Holy Spirit.
According to early church tradition, the author of Acts is Luke the physician, who traveled with the Apostle Paul (Col 4:14; 2 Tim 4:11; Phlm 24). The Gospel of Luke is also ascribed to him; this makes Acts his second volume about the story of early Christianity (Acts 1:1; see the “Introduction to Luke”). Four passages in Acts seem to indicate that the narrator is a firsthand witness of particular events he describes (Acts 16:10–17; 20:5–15; 21:1–18; 27:1–28:16)—which is fitting with Luke being the author.
Like the Gospel of Luke, the book of Acts is addressed to Theophilus, who might have provided financial support for Luke to write both books (Luke 1:3; Acts 1:1). Luke’s broader audience appears to have been people who were already Christians, or at least were interested in Christianity (Luke 1:4). Since the narrative of Acts ends with Paul’s captivity in Rome, it might have been written shortly after his arrival there, in the early to mid-60s AD. Another possibility is that Paul preaching the gospel in Rome provided a natural stopping point for the book because it showed that the church was fulfilling Jesus’ command to be His witnesses to the ends of the earth—Jerusalem and Rome were on opposite sides of the empire (Acts 1:8). In this case, Acts could have been written later in the first century AD."

—Faithlife Study Bible, Lexham Press