Here is the introduction to Matthew that I wrote for my Ugandan friends:
Matthew is the most Jewish of the Gospels. He prefers “Kingdom of Heaven” over “Kingdom of God.” (Because of the 3rd Commandment to “not take the name of the Lord in vain,” many Jewish writers would not say or write the word “God” for fear that they might take God’s name in vain.) Matthew has a deep interest in the Old Testament Law. The Gospel does not identify an author but from earliest times has been attributed to Matthew, the apostle and onetime tax collector (see Matthew 9:9). Little is known about when or where Matthew was actually written, and scholars date it as early as AD 50 and as late as AD 100. Matthew was not the first of the Gospels written (Mark is generally believed to be the first) but in the Canon it is listed first because the early church saw it as a link between the Old Testament and the New Testament. This linkage can be seen most clearly in Matthew 5-7, the Sermon on the Mount that links the old and new. Jesus repeatedly says “you have heard it said… but I say to you…” Matthew is also called the “ecclesiastical” Gospel, and its pages brim with concern for the life of the church.
Matthew’s connection to the Old Testament (he quotes the Old Testament more than any other Gospel writer) portrays Jesus as the promised Messiah, The Christ of God.