Matthew - Seems to be especially for the Jews, often pointing out the fulfillment of prophecy.
Mark - Short and vigorous record appealing to active Romans.
Luke - Literary masterpiece appealing to cultured Greeks.
John - Concentrates on things not already told.
John 20:31 - "But these are written that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name"