According to Tradition, after Pentecost St. Matthew preached the Good News of the Lord's Resurrection throughout Palestine. Then, at the request of the Jewish converts at Jerusalem, the holy Apostle Matthew wrote his Gospel describing the earthly life of the Savior before leaving to preach the Gospel in faraway lands. He then left to preach his Gospel in Syria, Media, Persia, Parthia, before being martyred in Ethiopia.
Because it was first recorded in Palestine, there is some speculation and evidence that Matthew's Gospel was originally written in Aramaic, though the earliest surviving version now in existence is in Greek. It was probably written somewhere from AD 60-65, though more liberal scholars put the date at 80-100.
The Gospel of St. Matthew is read liturgically over seventeen weeks beginning with the Monday of the Holy Spirit (the day after Pentecost). From the twelfth week, it is read on Saturdays and Sundays while the Gospel of St. Mark is read on the remaining weekdays.
Note that according to the Typicon, the Gospel of Luke always begins on the Monday following the Sunday after the Exaltation of the Cross. This may or may not be the 18th week after Pentecost. So the Gospel of St. Matthew readings may end before early (skipping readings) or later (repeting teadings).