The Acts of the Apostles is a book in which the Holy Spirit is especially prominent. The Spirit's activity dominates it. The book might well be called "The acts of the risen Christ by the Holy Spirit through the apostles."
It's important to note the progress in the believers' experience as the book moves from Jewish ground to the church.
Acts 2:38--Peter tells the Jews to repent, believe, and be baptized to receive the Spirit.
Acts 8:14-15--Peter prays for the Samaritans to receive the Spirit, lays hands on them, and they receive the gift of the Spirit.
Acts 10:44--The Holy Spirit comes on the Gentiles when they believe, and Peter can only stand by in amazement. Acts 10:44 is God's pattern for today; hear the Word, believe, receive the Spirit, and then be baptized as evidence of your faith.
It's quite clear from the book of Acts the Spirit is personal, for he did what only a person can be said to do. He spoke and caused others to speak. He bore witness, sent out Christian workers, forbade certain courses of action and appointed men to office in the church. He is associated with other persons and is clearly believed to be equal with God.
Agent of Christ
Acts 1:1 may imply that Jesus continued his work after the ascension through the Holy Spirit. He is the gift of the ascended Christ to his disciples and is called "the Spirit of Jesus." He is also described as "the promise of the Father."
Creator of the Church
The church as we know it was created at Pentecost. Wind and fire are Old Testament symbols of deity. The gift of tongues may have been deliberately chosen by God to symbolize the ultimate universality of the church, its presence among men and women of every language. The Spirit created a fellowship of love and unity, and he was promised to those who responded to the Christian message.
Uniting Force in Expanding Church
Luke is vitally interested in the progress of the gospel and the consequent expansion of the church through the activity of the Spirit. The church at Pentecost was composed of Jews and prosleytes; and Gentiles who were committed to Judaism and so reckoned as if they were Jews.
Jews hated Samaritans, who were of mixed race and schismatic religion, but in Acts 8:14-17 the Spirit came upon Samaritan believers. It's significant this happened only after the (Jewish) apostles had laid their hands on them, indicating an attitude of love and fellowship on their part as well as the fact that "salvation is from the Jews."
The barrier between Jews and Gentiles was broken down in Acts 10:44-48, when the phenomena of Pentecost were repeated by the Spirit as Peter preached the gospel to Gentiles.
It was through John the Baptist the promise of the Spirit had first been given, so Luke records how a group of John's disciples also received the Spirit (Acts 19:1-7).
Power Behind the Church
The Holy Spirit was given to the church to enable it to witness for Christ (1:8). The church was directed by the Spirit when they sent Barnabas and Saul to evangelize the Gentiles (13:1-4), just as he had earlier guided Peter to preach the gospel to Cornelius and his friends (10:19ff).
Filled with the Spirit they spoke with power (4:8, 31: 6:10) and undertook the various aspects of the new church's life and witness (6:3, 5; 11:22-24). The Holy Spirit gave people power to reveal Christ both by their lips and by their lives.
Life of the Church
The Spirit of God is concerned with the inner life of the church in every place (9:31). It was the Spirit who appointed elders of the church as its guardians (20:28).
The new age was to be one of prophecy (2:17-18), concerned with the instruction and building-up of the church and its people (15:32) and prediction of things to come (11:28).
The church in council sought guidance and believed this was given through the Holy Spirit (15:28).
So, Acts occupies a unique position in the revelation of the person and role of the Holy Spirit. The book records a fulfillment which is also a new beginning.
The prophecies of the Old Testament and the promises of the Lord Jesus about the Holy Spirit find their fulfillment at Pentecost.
The new age, the age of the Spirit, preached by Jesus, so evident in the Letters of the New Testament, had begun.
(Sources: Article by G.W. Grogan, Eerdmans' Handbook of the Bible: Wiersbe's Expository Outlines)