t is fairly much agreed that Mark was the first Gospel writer, and that both Luke and Matthew had a copy of Mark available to them as they wrote. We can see this because there's a good deal of material from Mark which is used in both Matthew and Luke.
However, both Matthew and Luke often depart from Mark's account - and when they do, they often do it in exactly the same way. This suggests that they had another source on which they were also drawing. We don't have a copy of this other source, or any idea who wrote it; clearly it wasn't an inspired account, and the Holy Spirit hasn't preserved it for us; scholars a century ago simply labelled it `Q' (for Quelle, the German word for `source'). It seems to come from an Aramaic background, which suggests that it goes right back to good, strong traditions close to Jesus and the Palestinian setting of the story. The existence of `Q' is still sometimes questioned, but it's accepted by most students of Luke.
In addition, Luke had other sources which he mentions in chapter 1. He seems to have done his own original research (and his travels with Paul had clearly brought him into contact with significant people in the Jesus story, eyewitnesses who were now scattered all over the map of the Empire). Because of some of the intimate family details he supplies, it has been suggested that he learned a good deal from Mary, the mother of Jesus. We don't know for sure who he spoke to, and what he got from them, but he seems convinced that he had uncovered valuable, reliable material, and that it came from people who possessed indisputable authority as witnesses.
He also remarks to Theophilus that many people have already tried to compile accounts of the Jesus events. `They used as their source material the reports circulating among us from the early disciples and other eyewitnesses of what God has done in fulfillment of his promises' (1:2, New Living Translation). Luke clains that he has `carefully investigated all these accounts from the beginning'; he has made himself an expert on the various accounts built on eyewitness tradition.
Click here to read more about Luke's process of composition.