The Q Source
According to many Biblical scholars, particularly and most notably starting with Nineteenth Century scholars, portions of Scripture called the Synoptic Gospels, involve a source called "Q."
Synoptic=taking the same point of view, or complimentary.
As the diagram shows (and in many scholars' opinions), Matthew and Luke both use arguments/material from Mark and from the "Q" author/source. Mark does not "take from" the "Q" source, and Matthew and Luke seem to not "take from" each other, although altogether, Mark, Matthew and Luke (and "Q") all are complimentary pieces which basically agree on major points.
Because the Matthew works and Luke works "take from" Mark material and because Mark seems to be a stand-apart set of works, many scholars believe the Mark Gospels were written first as the primary documents that Matthew and Luke draw from. (not my personal opinion - I believe Matthew may have been written first, but I this hub is about "Q" mainly and I am still researching to find out if my viewpoint is valid or not).
The Gospel of John is not considered a "peer" work that is shared by all the Gospel authors and the works attributed to John are considered separate or, at least, are dealt with separately by most scholars.
The "Q" Source: "Q" comes from the German word Quelle, meaning, "source." It is basically defined as a source of "common" material to be found in Luke and Matthew but not in Mark, as already explained above. A problem exists here, however, because Q Source is considered a hypothetical document...it is supposed to have contained the words - "quotations" - of everyone's favourite subject and persona - Jesus. The Q Source document is considered to have been separated from other compilations of text by the fathers of the early church as "Christianity" was being established. Later on, the early fathers of the church did not include the Q source in the overall body of the collection of scripures we now call "The Bible."
For more information on Q: The Sayings Gospel Q: collected essays by James McConkey Robinson, Christoph Heil, Jozef Verheyden (this is an open "Google Books" document). The link should take you right to the chapter, THE CRITICAL EDITION OF Q AND THE STUDY OF JESUS. This book appears to be entirely, legally visible through Google Books, more than 800 (almost 900) pages of information on the Q Source.
Competing Theories exist on all sorts of things related to this Q source, but most scholars, from varied Christian denominations - and scholars outside of Christian affiliation - at least do agree of the existence, in the past, of a "Q" source. (Even some lesser arguments hold their own in the explanation, simply, that "A whole BUNCH of documents exist" outside of what is commonly known as "Scriptures" and "The Bible" - that a general public is not aware of and that ancient scholars haven't told anyone about and libraries full of texts exist that church authorities did not choose to include in the volumes of works known as "The Bible." Many scholars aware of or who believe in this, automatically assume that "Q" is possible and should not be discounted). Most of the differing theories are concerned with which text was written first, in what particular order all the texts were written, or on possible agendas each author may have had for writing their text and for taking material from other texts.
The Hypothetical Case For Q:
Scholars interested in the existence of Q argue that other gospel texts, Matthew and Luke can exist independently, aside from shared material in Mark.
Part of this hypothesis asserts that, along with the point above, the verbal agreement between Matthew and Luke is extremely strong. From this agreement, it is assumed that, because Matthew and Luke do not "take from" each other to form the verbal agreements, there must exist another (Q) same source that Matthew and Luke both draw information from.
Supporters of the "Case for Q" believe that Matthew and Luke, although independent of each other, are dependent on the same other source - Q.
Also, in the text attributed to the author, Luke, this author states that he is aware of other sources written about Jesus' life and that he has essentially "investigated" in order to gain the most information possible on Jesus' life. It is believed, by scholars, that if Luke actually "researched" on the subject of Jesus, his words, actions, etc., then Luke probably came across many sources of good information about Jesus - and probably, also the Q document from the Q source.
The case for the existence of Q or a Q document is also made strong by the fact that it can be proven that a number of authors of Scripture weren't "original creators of literature" but were copyists and scholars. Therefore, much of what is attributed to certain authors is not their original ideas but the collective ideas of scholars - continually copied forward until a sanctioned volume of "Scriptures" was decided upon...which are supposed to be "the best of the best" works of ancient authors, those believed to be inspired by divine events and spirits, etc.