1. Author and time of writing
In the first verse of the book of Acts the author mentions the fact that he has already written an earlier report "concerning all things which Jesus began both to do and to teach, until that day in which he was taken up." The gospel of Luke, as well as the book of Acts, is addressed to a certain Theophilus (cf Luke 1:3). Therefore one would conclude that the book of Acts also originates from the pen of Luke.
Already the church father Ireneus (ca 140-202) mentions that Luke is the author of the book of Acts. Various scholars have also pointed out that the style and the choice of words in Luke and Acts are very similar.
In the book of Acts itself we find two important hints which are important to ascertain the time of writing. First of all Luke mentions the fact that Acts is the sequel to the Gospel of Luke (written around 55-60 AD), and therefore must have been written later. Secondly Luke at the end of Acts Luke mentions Paul's two-year imprisonment in Rome. The book will therefore have been written only after the end of this time. It is generally assumed that Paul came to Rome around 60/61AD. Therefore the earliest that the book of Acts could have been written would have been around 63. It cannot have been written much later as Luke would then have mentioned the result of the Paul's case, the fire of Rome and the first great persecution of Christians in 64.
Some scholars believe that chapter 5:36 and 11:28 are quotes from or similarities to Flavius Josephus' work "The antiquities of the Jews". Since Josephus wrote in the last decade of the first century the book of Acts would have been written even later. But it is very unlikely that Luke copied from Josephus, and therefore this idea is held by only few scholars nowadays.
2. Subject and purpose of writing
As already mentioned, the book of Acts is the second part of a work by which the author wants to give an important person an overview over the beginning of Christianity, i.e. life and death of the redeemer and the beginning of the spreading of the Christian faith.
The title "Acts of the Apostles" does not very well reflect the intention of God, who inspired Luke to this report. A better title would be "The Acts (or the workings) of the Holy Spirit", because He is the real main character of the book. The presence and working of the Holy Spirit is the dominating mark of the book of Acts.
The book of Acts also describes the work of the two apostles Peter and Paul. Peter is the human main character in the first 12 chapters, Paul in the second part from chapter 13. The geographical centre of the first part is Jerusalem, of the second Antioch, where the first great assembly of converted heathens was formed.
Luke does not mention his own name at all, although he accompanied Paul on more than one journey, which can be concluded from the so-called "we-paragraphs". On the first journey to Asia minor (around 46-49 AD) Paul was accompanied by Barnabas (Acts 13:1 - 15:33), on the second journey to Asia minor and Greece (around 51-54 AD) by Silas (Acts 15:40-18:22); later Timothy joined them (Acts 16:1-3), and in Troas Luke joined them for the first time (Acts 16:8-10 - "we"). Then Luke stayed at Philippi (Acts 16:40 - "they"). When Paul came again to Philippi on his third journey (around 54-58AD, Acts 18:23 - 21:26) Luke was still there, because now we have another "we-paragraph" (Acts 20:5-21:10). Now Luke accompanies the apostle again to Jerusalem. Finally, he belonged to those who sailed with Paul from Cesarea to Rome (Acts 27:1-28:16).
The book of Acts is the link between the Gospels and the Epistles. Its subject and intention is nicely summarised by the words of the Lord in chapter 1:8: "But ye will receive power, the Holy Spirit having come upon you, and ye shall be my witnesses both in Jerusalem and in all Judaea and Samaria and to the end of the earth."
3. Overview of Contents
I. Acts 1-12: The service of the Apostle Peter in Jerusalem, Judaea and Samaria
II. Acts 13-28: The service of the Apostle Paul in the whole world