Gospel of Matthew
The Gospel of Matthew is the first book in the New Testament, as one of four gospels. It tells the story of the life of Jesus as conveyed by Matthew, a former tax collector and one of Jesus' disciples. Several of the parables recounted in this Gospel rely on economic principles.
The Gospel of Matthew is one of the synoptic gospels, meaning that it is written in a narrative style and has similarities to the Gospels of Mark, and Luke. The three share a common structure which shows an interrelationship. It is generally believed today that the simpler Gospel of Mark came first, and then Matthew and Luke benefited from having seen that Gospel before completing their own. But church tradition held that Matthew came first and some still support that sequence. There is reference by the church fathers to a Gospel of Matthew originally being written in Aramaic, perhaps based on a theory that Jesus taught in Aramaic rather than Greek. But no Aramaic original for the Gospel of Matthew has ever been found, so it appears likely it was initially written in Greek which an educated former tax collector could surely have done.
The Gospel of Matthew ends with the Great Commission, commanding those of Christian faith to baptize and evangelize all the peoples of the world: "And Jesus came and spoke to them, saying, "All power is given unto Me in heaven and in earth. Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen." (Mat 28:18-20, King James Version).
The Gospel of Matthew does not name its author, but the ancient church fathers were unanimous that the author was Jesus' disciple Matthew. Mark and Luke both use the name Levi, Matthew's other name, but the book of Matthew does not.
In the second century, the Church Father Saint Irenaeus records that St. Matthew wrote the First Gospel and that the Four Gospels were already universally accepted by the Christian Church as Inspired Scriptures: "We have learned from none others the plan of our salvation, than from those through whom the Gospel has come down to us, which they did at one time proclaim in public, and, at a later period, by the will of God, handed down to us in the Scriptures, to be the ground and pillar of our faith ... Matthew also issued a written Gospel among the Hebrews in their own dialect, while Peter and Paul were preaching at Rome, and laying the foundations of the Church. After their departure, Mark, the disciple and interpreter of Peter, did also hand down to us in writing what had been preached by Peter. Luke also, the companion of Paul, recorded in a book the Gospel preached by him. Afterwards, John, the disciple of the Lord, who also had leaned upon His breast, did himself publish a Gospel during his residence at Ephesus in Asia." Saint Matthew the Apostle therefore wrote in the lifetime of Sts. Peter and Paul, and St. Mark shortly thereafter wrote his own Gospel based on the preaching of St. Peter.
Archbishop St. John Chrysostom of Constantinople gives an additional reason why Four Evangelists wrote, rather than just one. "5. And why can it have been, that when there were so many disciples, two write only from among the apostles, and two from among their followers? (For one that was a disciple of Paul [i.e. Luke], and another of Peter [i.e. Mark], together with Matthew and John, wrote the Gospels.) It was because they did nothing for vainglory, but all things for use. What then? Was not one evangelist sufficient to tell all? One indeed was sufficient; but if there be four that write, not at the same times, nor in the same places, neither after having met together, and conversed one with another, and then they speak all things as it were out of one mouth, this becomes a very great demonstration of the truth." This is in accord with the ancient Biblical principle that "at the mouth of two witnesses, or at the mouth of three witnesses, shall the matter be established" (Deut 19:15).
The Church Father Saint Jerome wrote: "Matthew, also called Levi, apostle and aforetimes publican, composed a gospel of Christ at first published in Judea in Hebrew for the sake of those of the circumcision who believed, but this was afterwards translated into Greek, though by what author is uncertain. The Hebrew itself has been preserved until the present day in the library at Cæsarea which Pamphilus so diligently gathered. I have also had the opportunity of having the volume described to me by the Nazarenes of Berœa, a city of Syria, who use it. In this it is to be noted that wherever the Evangelist, whether on his own account or in the person of our Lord the Saviour quotes the testimony of the Old Testament he does not follow the authority of the translators of the Septuagint but the Hebrew. Wherefore these two forms exist Out of Egypt have I called my son, and for he shall be called a Nazarene."
The C.E. summarizes: "About the middle of the third century, the Gospel of Matthew was received by the whole Christian Church as a Divinely inspired document, and consequently as canonical. The testimony of Origen ("In Matt.", quoted by Eusebius, Church History III.25.4), of Eusebius (op. cit., III, xxiv, 5; xxv, 1), and of St. Jerome ("De Viris Ill.", iii, "Prolog. in Matt.,") are explicit in this respect. It might be added that this Gospel is found in the most ancient versions: Old Latin, Syriac, and Egyptian. Finally, it stands at the head of the Books of the New Testament in the Canon of the Council of Laodicea (363) and in that of St. Athanasius (326-73), and very probably it was in the last part of the Muratorian Canon. Furthermore, the canonicity of the Gospel of St. Matthew is accepted by the entire Christian world." 
Matthew writes to Jews. In his attempt to convince Jews that Jesus was the Messiah, he has more quotations from the Old Testament than any other gospel (especially in regards to fulfillment of prophecy), he uses Jewish terminology, and he traces the lineage of Jesus back to Abraham.
The Apostle quotes the Torah/Old Testament in the First Gospel no less than 65 times.. The Gospel is remniscent of those early days of Christianity where the Apostolic Church remained very close to its Hebrew roots.
Place of Writing
There are different thoughts on when it was written. If Mark was written first, then depending upon when Mark was written, Matthew would have to have been written after it. Dates from the late 50's all the way to the 70's or beyond are speculated. Some believe that based on the Jewish character of Matthew, that it must have been written when the church was still mostly Jewish, and so they believe it was written in 50 or so and was the first gospel subsequently drawn upon by Mark and Luke.
The purpose of Matthew is to show that Jesus is the Messiah who has come according to the Old Testament scriptures. Indeed, Matthew includes 9 additional proof texts that the others Gospels do not. Matthew is also known for the use of sermons, such as the sermon on the mount. It is these sermons that contribute to Matthew's size more than the any extra content or stories within the text.
- Against Heresies, Book III, Chapter 1, Saint Irenaeus. http://www.newadvent.org/fathers/0103301.htm
- Homily 1 on Matthew, Saint John Chrysostom: https://www.newadvent.org/fathers/200101.htm
- De Viris Illustribus, 3:1 (On Illustrious Men), St. Jerome https://www.newadvent.org/fathers/2708.htm
- Catholic Encyclopedia, Gospel of St. Matthew. https://www.newadvent.org/cathen/10057a.htm
- Gospel of St. Matthew, Introduction. Henry, Fr. Basil. https://stlukeanniston.org/files/Gospel-of-St.-Matthew---Introduction.pdf