For years, most biblical scholars followed the Augustinian hypothesis. St. Augustine (354-430) held that the Gospel of Matthew was the first to be written. The Gospel of Mark then used Matthew in the writing of his gospel. Then the Gospel of Luke followed both Matthew and Mark with his gospel. Finally, the Gospel of John was quite different from the other three. Thus, the first three were called the synoptic gospels. This is the order that you find in most bibles.
One of the earliest attempts at solidifying a Christian canon or list of books was made by Marcion of Sinope (85-160 CE). He rejected the Hebrew Scriptures, so that other Christian leaders denounced him. Thus, he was excommunicated from the proto-orthodox Christian Church community. However, he was the first to publish his own list of New Testament books around the year 140 CE, that included 10 letters of Paul and the Gospel of Luke.
There are four canonical gospels that have been ascribed to various individuals. The Gospel of Matthew, from around 70-100 CE, was attributed to Matthew, the apostle. The Gospel of Mark, from around 60-70 CE, was attributed to a companion of Peter called Mark. The Gospel of Luke, from around 80-90 CE, was considered to be a traveling companion of Paul. The Gospel of John, from the later 90-100 CE, was attributed to the apostle of Jesus named John.