This gospel is generally considered the work of Luke. Specifically, Luke the Gentile by birth, well educated in Greek culture, physician by profession, a companion of Paul at various times from his second missionary journey to his final imprisonment in Rome, and, according to the letter to Timothy, a loyal friend who remained with the apostle after others had deserted him.
There are movements in Acts from the which begin with "We..." These are likely to be personal memoirs of one of Paul's companions but there is no change in style to indicate these are from a different writer than Luke.
From the second century on, church leaders universally refer to that Luke as the author. The same Luke wrote both Luke and Acts and the two should be considered a continuous chronology by the author, Luke detailing the life, work, death, and resurrection of .Jesus and Acts detailing the growth and work of the Church.
While there is no specific event that prompts the writing of the gospel, the intent, as given in the preamble is to give an orderly account of the life of Jesus and to inspire belief in Jesus as the Christ for the reader. While "orderly" does mean in the sense of being a logical whole, it does not necessarily mean in exact chronological order of the events.
Luke was written in about 58-60 C.E. It makes no reference to Nero's persecution of the Church in 64/65 C.E. and also no mention of the Jewish revolt in 66 C.E. but does refer to a destruction of Jerusalem. Jerusalem was destroyed in 70 C.E. but scholars are divided as to whether the reference was looking back or part of a general kind of warning.
Luke speaks of the need for sharing the Good News of Christ and may also be intended to help deal with the "delay" in the Second Coming. There are parables and references to a delayed return of a master.
There is also no specific location in mind for Luke to be heard. Luke wrote the Gospel in Rome or possibly in Caesarea. Settings in the book include Bethlehem, Jerusalem, Judea and Galilee.
The preamble of the book is addressed to "Theophilus." This may refer to a specific person who is given the prefix "Most Excellent," the same as used for Felix and other Roman officials. It may be that Theophilus is not a specific person, but rather a nickname for all who love God. (The name means "one who loves God.")
Luke is written from a perspective where the synagogue and the Church are or are becoming separate. It has in mind Gentile readers as many Jewish practices are explained and the prophecies cited refer to "all flesh."
The gospel highlights Jesus care and concern for the poor, women, foreigners, and others who were on the fringes of Jewish and Roman society of the time.