Who was Matthew?
The Gospel writer was a carpenter. ( Mt 9.9-13 ) Papias ( cited by Eusebius, Ecclesiastical History 3.39.16 ) shows that Matthew compiled the sayings ''λόγια', in the Aramaic/Hebrew Language, and translated them as well as he could.
When was the Gospel written?
Uses Mark, knows of fall of Jerusalem, therefore post 70. Known by Ignatius, c.110-115, so probably was finally written and in circulation by the 80's and 90's.
Comparison with Mark:
The Gospel follows the same general pattern, although Matthew adds birth stories, more on the resurrection story, and five blocks of teaching ( linking to the Torah ).
The Birth stories show Jesus as the Son of David, Son of God, second Moses, and Emmanuel ( God is with us ).
The fall of Jerusalem is proof of God' wrath on Israel perhaps, and the tension can be seen in the Gospel, between Matthew's community and the local Synagogue. For Matthew, the Church is the new Israel, heir to all God's promises in the Old Testament.
Christ as 'the new Moses' :
The outline of the Lord's ministry, has close parallels to that of Moses:
1) Male child miraculously born to Jews
2) A fierce tyrant ( Herod ) wants to destroy Him
3) Child supernaturally protected from harm in Egypt
4) Passes through waters - Baptism
5) Goes into wilderness
6) Goes up a mountain to deliver God's law
These early stories show that He is a fulfilment of the story of Moses. Herod is like the Pharaoh. Christ experiences forty days of testing, like the forty years children of Israel spent in the wilderness. Moses was also rejected by those who refused to recognise his leadership, so too was Jesus.
Perhaps most importantly, the Sermon on the Mount, is like the law of Moses being delivered on Mount Sinai. Jesus is therefore the one Who Has come to set His people free, through all of these fulfilment's. Christians are expected to follow the traditional Jewish cultic practices, however they are of secondary importance. The law is to be obeyed to the fullest extent possible, but what really matters is Christ and His life and love. This of course brings in the idea of Christian life being compatible with Jewish tradition, as well as being a fulfilment of that tradition. Furthermore it highlights that Christ is the true life, regardless of culture and situation. It is important to note that Christ does not replace Moses. Rather, He is the true and final interpreter of what Moses recorded in the law - followers must obey the Old Testament laws, as prescribed by Christ. The Lord's sermon provides guidance, and true understanding of Jewish law.
Genealogy: Mt 1.2-17
Traced back to Abraham, two sets of fourteen which is Gematria ( an Assyro-Babylonian system of numerology, later adopted by Jews which assigns numerical value to a word or phrase ) based on 'David'.
Mary found to be pregnant: Mt 1.18-25
Betrothal, around 12.5 years old; same legal status as marriage, so therefore it was presumed by some that she had been involved in an affair, therefore adultery. This is where the first of many dreams are said to have taken place, as well as first of many Old Testament citations. Joseph does not have any relations with Mary until the Birth, showing the baby certainly isn't his.
Visit of Magi: Mt 2.1-12
Jesus is born in Bethlehem ( city of David )
Magi, astrologers from the east, Perians, Zoroastrians.
This reflects the prophecy of Balaam ( Numbers 22-24 )
Herod and all of Jerusalem - anticipation of hostility at the end of the Gospel.
Egypt and on to Nazareth: Mt 2.13-23
There is a contest between Herod and the Magi.
Egypt - parallel with Moses; as well as the story of Israel.
Herod is seen as the Pharaoh ( Exodus 1 )
An interesting point that scholars make, is that perhaps Matthew intended this section to be a poetic introduction to the themes that would later emerge in his Gospel. His account of the Birth , seems to be very different to Luke's account, and of course Matthew is concentrating on the Old Testament prophecies, as well as dreams. This is why scholars argue that his account was perhaps not a historical one.
Beatitudes: Mt 5.3-12
Blessings in the future age, reminiscent of Isaiah 61.1, 2,7
Jesus and the Law: Mt 5.17-20
Prologue to the six examples which Christ then gives. Matthew's community is of course not only still keeping the Jewish law, but also going beyond it; surpassing the Mosaic Law. Christ therefore is in continuity with what went before, but also as Messiah brings the renewal.
Six Examples: Mt 5.21 - 5.48
The Lord gives six concrete examples of the kind of attitude that He expects. It is moral vision, rather than a set of rules. Murder, adultery, divorce, oaths, turn the other cheek, love of enemies. Much of this has parallels with rabbinic literature; again highlighting how Jesus the Messiah is teaching the truth, a truth that is expressed fully and perfectly in Him and through Him. Matthew highlights that Jesus speaks with authority, as the New Moses, bringing renewal to the law.
Instruction on how to act: Mt 6.1-18
Almsgiving, prayer, fasting; central thing is the intention. The Lord's Prayer is also given ( which has parallels to Shemoneh Esreh )
Overall, the Gospel of Matthew recognises Jesus as a Jewish Messiah ( as Matthew is writing especially for the Jews ), and that He instructs the people if Israel to follow Jewish tradition in the right way - but of course it also urges them to reject the Jewish authorities.