As a fellowship, we recently started a study of the Acts of Apostles and are presently in Chapter 9. This post will be a brief introduction to The Acts of Apostles and then subsequent posts will follow the lessons we have learnt so far.
The author is identified as Luke the Physician and seen as a sequel to the Gospel according to Luke: “In the first book, O Theophilus, I have dealt with all that Jesus began to do and teach, until the day when he was taken up, after he had given commands through the Holy Spirit to the apostles whom he had chosen.” (Acts 1:1-2). The reference to “the first book” is the Gospel according to Luke as has been said earlier. So Acts can be viewed as a sequel to The Gospel According To Luke (Luke 1:1-4).
According to early church tradition, the book of Acts was written by Luke the Physician, a companion of Paul on his second and third missionary journeys and on the voyage to Rome. Irenaeus, Clement of Alexandria, the anonymous Muratorian Canon, and Eusebius all credit Luke as the author. 
The recepient is also clearly identified in the prologue as Theophilus: “In the first book, O Theophilus…” (1:1). According to John MacArthur,
Theophilus, whose name means “lover of God,” is unknown to history apart from his mention in Luke and Acts. Whether he was a believer whom Luke was instructing or a pagan whom Luke sought to convert is not known. Luke’s address of him as “most excellent Theophilus” (Luke 1:3) suggests he was a Roman official of some importance (cf 24:3; 26:25). 
Why Acts Was Written
As was identified earlier, Acts is a sequel to the gospel according to Luke and it was written primarily to instruct Theophilus, its receipient about the life of Christ after his ascension. The author identifies that, in the first book, he “dealt with all that Jesus began to do and teach, until the day when he was taken up, after he had given commands through the Holy Spirit to the apostles whom he had chosen.”(vv.1-2). This means that Acts was written primarly to chronicle events after Jesus’ ascension and the work of the Holy Spirit through the Apostles in the early church. That makes clear sense why it is then calles “The Acts of The Apostles.”
What We Can Learn From Acts.
As a narrative, we can learn about the life of the early church and its involvement in Missions. In the book of Acts we see how the Apostles engaged their communities through the power of the Holy Spirit. Most importantly, as we read and study the book of Acts, we come face to face with the reality of the person of Christ and his saving grace. It is in Acts we see the powerful proclamation of the exclusivity of Christ for salvation: “And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved.” (Acts 4:12).
As believers, the book of Acts is a great example of a book to stir us up to engage our community with the gospel of Christ.
1. R.C. Sproul, The Reformation Study Bible NKJV (Orlando: Florida, Reformation Trust, 2016), 1996
2. John MacArthur, The MacArthur Bible Commentary (Nashville, Thomas Nelson, 2005), 1430