Luke is the author, although he is not mentioned by name in the book. We know the author was a companion of Paul because he uses “we” in several passages (Acts 16:10-17; 20:5-15; 21:1-18; 27:1-28:16).
There are 50 or so words and phrases that are used in both Luke and Acts that do not appear elsewhere in the New Testament.
Luke was probably a Gentile (Colossians 4:11-14) — He is distinguished from those “who are of the circumcision.”
Luke was a physician (Colossians 4:14) and uses technical terms to describe diseases and other physical conditions throughout Luke and Acts.
The Acts of the Apostles was not the title given to the book by Luke, but it is found as early as late second-century manuscripts.
Acts is a continuation of Luke.
Inasmuch as many have taken in hand to set in order a narrative of those things which have been fulfilled among us, just as those who from the beginning were eyewitnesses and ministers of the word delivered them to us, it seemed good to me also, having had perfect understanding of all things from the very first, to write to you an orderly account, most excellent Theophilus, that you may know the certainty of those things in which you were instructed (Luke 1:1-4).
The former account I made, O Theophilus, of all that Jesus began both to do and teach, until the day in which He was taken up, after He through the Holy Spirit had given commandments to the apostles whom He had chosen, to whom He also presented Himself alive after His suffering by many infallible proofs, being seen by them during forty days and speaking of the things pertaining to the kingdom of God (Acts 1:1-3).
Suppose again the Epistles were there, but [Acts] left out, how startling would appear the heading “To the Romans,” which would confront us on turning from the study of the Evangelists! How could we account for the transition involved? How could we explain the great thesis of the Epistles, that there is no difference between Jew and Gentile … ? The earlier Scriptures will be searched in vain for teaching such as this. Not the Old Testament merely but even the Gospels themselves are seemingly separated from the Epistles by a gulf. To bridge over that gulf is the Divine purpose for which [Acts] has been given to the Church. The earlier portion of the book is the completion of and sequel to the Gospels; its concluding narrative is introductory to the great revelation of Christianity. — The Silence of God, by Sir Robert Anderson, pages 54-55.
The following is a timeline taken from The Acts of the Apostles, by Thomas Walker (pages xxvi – xxviii). I haven’t studied enough to know how accurate it is, but I include it for reference sake.
30 A.D.
Our Lord’s ascension
Day of Pentecost
36
Martyrdom of Stephen
Philip in Samaria
Conversion of Paul (If the “fourteen years” of Galatians 2:1 do not include the “three years” of Galatians 1:18, the date of Paul’s conversion must be thrown back to A.D. 33 or 34.)
36-38
Paul in Arabia and Damascus
38
Paul in Jerusalem (first visit)
Departure to Tarsus
38-43
Paul’s work in Syria and Cilicia (Galatians 1:21)
Peter at Lydda, Joppa and Caesarea
Conversion of Cornelius
Hellenists preaching at Antioch and Barnabas’ work there
43 or 44
Paul at Antioch with Barnabas
44
Martyrdom of James
Death of Herod Agrippa I
46
Paul at Jerusalem (2nd visit) with Barnabas, carrying alms from Antioch
47 (early)
Paul returns to Antioch with Barnabas
47 (spring to summer)
First Missionary Journey — Cyprus, Pisidian Antioch, Iconium, Lystra, Derbe, return to Antioch, via Perga
50 (early)
Paul at Jerusalem (third visit) with Barnabas
50 (spring)
Return to Antioch. Separation from Barnabas
50 (summer) to 53 (early)
Second Missionary Journey
50-51
Paul and Silas in Syria, Cilicia and Asia Minor. Timothy. Troas. Arrival of Luke
Philippi, Thessalonica, Berea, Athens
51 (September ?) to 53 (early)
At Corinth. Writes 1 Thessalonians. Writes 2 Thessalonians
53 (early)
Return to Palestine via Ephesus
Paul at Jerusalem (fourth visit) short
53 (spring) to 57 (May)
Third Missionary Journey
53 (summer)
Work in Galatia – Phrygia
53 (autumn) to 56 (early)
Work in Ephesus
Writes 1 Corinthians (end of stay)
56 (summer and autumn)
Work in Macedonia
Writes 2 Corinthians
Writes Galatians (?)
56 (December) to 57 (February)
Work in Corinth
Writes Romans
57 (April)
Travels via Philippi
57 (April – May)
Return to Jerusalem, via Troas, Miletus, Tyre and Caesarea
57 (May)
Paul at Jerusalem (fifth visit). Arrest in temple. Speeches to people and Sanhedrin
Sent to Caesarea by Claudius Lysias
57 (summer) to 59 (summer)
Paul at Caesarea, a prisoner. Felix, Festus, Herod Agrippa II
59 (late summer)
Paul’s voyage to Rome
59 (November) to 60 (February)
Shipwrecked in Malta
60 (spring)
Arrival in Rome via Puteoli
60 (spring) to 62
Paul’s first Roman imprisonment. Writes Philippians, Colossians, Philemon and Ephesians
62 (spring)
Release from captivity
62 to 65
Paul’s last labors in Spain (?), Crete, Greece and Asia Minor
Writes 1 Timothy, Titus
65 to 67
Paul’s second Roman imprisonment. Writes 2 Timothy
67
Paul’s martyrdom
The reference books I used at the beginning of my study of Acts are as follows. (My library may change if I find other useful books or decide one of these isn’t worth the time.)
The Acts of the Apostles, by Thomas Walker (Moody Press, 1965)
Acts Dispensationally Considered, by C.R. Stam (Berean Bible Society, 1954)
The Acts of the Apostles: An Exposition, by Arno C. Gaebelein (Our Hope Press, 1912)
Lectures on the Book of Acts, by H.A. Ironside (Loizeaus Brothers, Bible Truth Depot, 1943)
The Acts of the Apostles, by G. Campbell Morgan (Fleming H. Revell Company, 1924)
King James Bible Commentary (Thomas Nelson Publishers, 1983)
The New Testament: An Expanded Translation, by Kenneth S. Wuest (William B. Eerdmans Publishing Company, 1961