The traditional order, sometimes called the Augustinian order, is Matthew, Mark, Luke. The sequence most commonly advocated today in Bible commentaries, both Catholic and Protestant, is Mark, Matthew, Luke, with Matthew and Luke being understood as more or less simultaneous. This sequence, known as “Markan priority,” may be nearing collapse as an intellectual construct. To back it, a scholar needs to ignore most external evidence regarding the order of the synoptics—that evidence favors the traditional order—and he needs to believe in the existence of a “sayings source,” a first-century document supposedly used by Matthew and Luke to fill in the gaps in Mark’s account. The Gospel by Mark, being the shortest and simplest, leaves out much material that appears in Matthew and Luke (and sometimes in Matthew or Luke). If Matthew and Luke depended on Mark, they also must have depended on some other source for their extra information.
This other source is commonly referred to a “Q,” from the German Quelle (“source”). The problem is that no ancient document quotes from or even alludes to Q, and no more recent manuscript claims to be a transmittal of it. Thus Q is entirely an intellectual construct, something posited to shore up the major weakness in the Markan priority theory. Some scholars claim to have discovered not a unified Q, but one made of multiple strands, perhaps as many as four, which means they presume the existence of four documents, even though there is no external evidence for even one of them.
The theory of Markan priority seems to be losing ground rapidly. Prof. William Farmer, one of the world’s top biblical scholars and a fairly recent convert to the Catholic faith, wrote a book examining why so many scholars hold on to a theory that is now seen to have glaring weaknesses. He thinks they won’t be holding on to it for too much longer. Like the Ptolemaic theory, the Markan priority theory eventually will be junked.