Key Themes
Jesus the King
Matthew's first words call Jesus "the son of David," and the royal thread runs to the end. The Magi ask for "he who is born King of the Jews" (2:2). Jesus enters Jerusalem as the king of Zechariah 9:9 (21:5). The charge over the cross reads "This is Jesus, the King of the Jews" (27:37). And the risen Jesus claims "all authority in heaven and on earth" (28:18). The kingdom he preaches is his own.
Fulfillment
Matthew reads the Old Testament as a book of promises that Jesus keeps. The birth fulfills Isaiah, the return from Egypt fulfills Hosea, the ministry in Galilee fulfills Isaiah again, the healings fulfill Isaiah 53, the parables fulfill the Psalms, the entry fulfills Zechariah, and the betrayal money fulfills the prophets. Jesus does not replace the Scriptures; he completes them (5:17).
The Kingdom of Heaven
The phrase occurs about thirty times, and only in Matthew. The kingdom is "at hand" (4:17), it belongs to the poor in spirit (5:3), it grows like a mustard seed (13:31), it is worth selling everything for (13:44 to 46), and its keys are given to Peter (16:19). It is God's rule, breaking in through Jesus, to be completed at the end of the age.
Righteousness that exceeds
Matthew uses the word "righteousness" more than the other Gospels combined. Jesus is baptized "to fulfill all righteousness" (3:15), and he tells his disciples that unless their righteousness exceeds that of the scribes and Pharisees they will not enter the kingdom (5:20). The Sermon on the Mount then shows what that deeper righteousness looks like: not only no murder, but no contempt; not only no adultery, but no lust; not only love for neighbours, but love for enemies.
The church
Matthew is the only Gospel to use the word "church" (16:18; 18:17). Chapter 18 is a manual for life together: humility, care for the straying, how to deal with a brother who sins, and forgiveness without limit. The book ends not with Jesus departing but with Jesus promising to stay: "I am with you always, even to the end of the age" (28:20).