The Book Of Acts is addressed to the same man as that in the Book of Luke. While Luke's name is not found in Acts, it is possible, and logical, that he could also have been its author.
While not a great amount is known of Luke personally, we are told that he was a doctor, a fellow-worker with Paul (see On The Road To Damascus), and that he alone stayed in support of Paul at the end - Paul wrote in 2 Timothy 4:11, shortly before his being martyred in Rome during the time of Emperor Nero, that "only Luke is with me." The others left either for reasons of personal safety, or perhaps because of Paul's intense personality which would have been stressful to most people. Luke was obviously a very brave, loyal and faithful man. We would be very fortunate to have Luke for a friend - but of course, one day we will.
Some believe that Luke was from Antioch, due to his numerous familiar mentions of it in his writing. He apparently later lived in Philippi. Luke may well have been a Greek, and was almost certainly a Gentile.
There are also indications that Luke was a good friend of Mary, the mother of Jesus Christ, for a number of years, at Jerusalem, or elsewhere. Mary could well have been a source for at least some part of the book of Luke, which would explain how he obtained much of the detail in his writing. It is quite possible, and very likely, that Mary supplied much information to the Gospel writers.
An early anonymous source wrote of Luke after his death: "He served The Lord without distraction, having neither wife nor children, and at the age of 84 he fell asleep in Boeotia, full of The Holy Spirit." There are at least two accounts of how he died - see What Happened To The Apostles?
Fact Finder: Who did Luke address the Gospel of Luke to?
(a) Paul (b) Matthew (c) Theophilus (d) Diotrephes
Luke 1:3