John's Gospel seems to be primarily evangelistic.  Rather than carefully detailing what Jesus did and said (as the other Gospel writers did) John selected only a few limited events from Jesus' life and used them to demonstrate conclusively that Jesus was indeed God and Savoir.  John totally ignored the manger scene, the wise men, the shepherds; he wasn't very interested in Old Testament prophecy either.  He presented Jesus full-grown--selecting so few events from Jesus' life that they might have filled up only a few weeks.  He certainly was not interested in maintaining chronological sequences, but went to great lengths to establish beyond reasonable doubt that Jesus is God himself in human flesh--the sole source of life, and illumination of Truth.  He used the word, "life" 36 times (twice any of the other Gospel writers).

Luke, on the other hand, systematically and chronologically sets forth Jesus’ humanity--beginning with his family, his birth, and early events in Jesus' life.  He records Jesus' genealogy all the way back to the very first humans to prove that humanity.  His main themes include the recognition of Gentiles in God's plan of salvation, emphasis on prayer, special concern for women and the poor, and he repeatedly uses the title "Son of Man" as applied to Jesus. 

Mark pictures Jesus as the suffering servant--and the reader almost becomes breathless following Jesus rushing place to place to serve the needs of everyone he encounters.   One Greek word--translated variously as "at once," "immediately," "quickly," or "just then"--is used 47 times to convey this feeling of immediacy.  Although Mark records less of Jesus' actual teachings, he uses "Rabbi", "teacher", or some form of these words 39 times in his short account.    Mark explains Jewish customs and events to his readers, so he probably assumes they will be Greek-speaking Gentiles not really acquainted with Jewish custom or history.  

Finally, Matthew  presents the Jewish Messiah to the nation that rejected Him—the royal king, and rightful heir to the throne of David.  Matthew details Messiah’s legal claim to the throne through Joseph's genealogy, and makes more appeals to literal fulfillment of Old Testament (Jewish) prophecy than any other Gospel writers. This would not impress many except Jews.  Few believed, or even knew, the Old Testament prophecies of the Messiah and his kingdom--except for the Jews.  But to the Jews--anticipating the expulsion of the Romans and the establishment of that kingdom--Matthew explains why Jesus was not exactly who they were expecting, and why Messiah’s promised kingdom was temporarily postponed.

Matthew's writing so serves as a bridge between the Old and New Testaments that many scholars and early church fathers believed it was the first Gospel written--that’s the reason why it was placed first in the New Testament canon!

More than any other of the Gospels, Matthew's is allied with the Hebrew Scriptures in theme and tone; their subjects are its subjects, the Messiah, Israel, the Law, the Kingdom, the Prophecy.  Jewish ideas and terms characterize the whole record.  Its witness would not have impressed either the Roman, for whom Mark wrote, or the Greek, for whom Luke wrote, but to Jews its significance would be inescapable.  [A Guide to the Gospels, Graham Scroggie]