The author has not been positively identified although Luke was a close friend of Paul. It was probably written around 90 AD and in very precise Greek language. It was also written after Mark since Luke makes references to Mark. In addition, the person who wrote Luke also wrote the Acts, since they are in a similar style.
Luke was written in a very analytic and documentary manner. It was the only gospel that chronicled the birth of Christ (the Magnificat) and the history of John the Baptist. This is why the early church supported the idea that Luke was a physician, due to the language he used and the precise nature of his writings. Luke's audience were the more educated members of the population, since they were the ones likely to have a knowledge of the language he used.