An Overview of Matthew's Gospel

Matthew, also called Levi, was a Jew and a tax collector (according to tradition) and therefore a tainted, compromised member of the Jewish community, a devious individual who made money by working for the Roman masters. His calling to follow Jesus is recorded all three Synoptic Gospels, in Matt 9: 9-13, and in Mark 2: 13-17, and also in Luke 5: 27-28. (In Mark and Luke, Matthew is identified by an alternate name, probably his birth name, Levi.)

Matthew's gospel is a letter written by a Jew, aimed at a Jewish audience.  The writer takes pains to record Jesus's lineage from the ancient king, David, and quotes various Old Testament passages to demonstrate Jesus's fulfillment of Messianic prophesies.

The account of Matthew is similar to that of Mark and Luke and so probably takes advantage of a common source for some details, most likely the gospel of Mark.

The Bible project has two short videos on Matthew, giving a nice overview.  They are both less than 10 minutes and are very well done!  Take a moment to watch these!
Overview of Matthew, Part 1
Overview of Matthew, Part 2

This overview divides the central core of the gospel of Matthew into 5 parts. Before these five sections is an introduction (Matthew 1-3) where Jesus is portrayed as the promised Jewish Messiah.

Then there are five sections, each with a discourse or teaching.  The five sections might be arranged to parallel the five Old Testament books of the Torah.

Here are the five parts, as suggested by the Bible Project.

1. Matthew 4-7, announcing the arrival of the Kingdom of Heaven.
2. Matthew 8-10, Jesus as healer of the new kingdom
3. Matthew 11-13, The people's response to the Messiah
4. Matthew 14-20, The reality of the servant Messiah
5. Matthew 21-25, The class of two kingdoms.

At the end, chapters 26-28, there is the celebration of the Passover, followed by trial, crucifixion and resurrection.

The summary of each of the 28 chapters of Matthew, as Twitter tweets, is available here.