THE SYNOPTIC PROBLEM
The so-called Synoptic Problem arises out of several factors: 
The "Synoptic Gospels" refer to the first three Gospels:  Matthew, Mark, Luke.
The term Synoptic derives from two Greek words, syn = together, and optic = to see.  The word "synoptic," therefore, has reference to the fact that the three Gospels see the story of Jesus through the "same eyes" or from the same vantage point or perspective.  They follow the same basic chronology.
For detailed discussion on this point click on Synoptic Gospels.

The "Problem" arises from both the similarities between the three Gospels, and their differences.
Questions relate to how one explains the striking similarities: Which one came first?  In what order were they written? 
Questions also relate to how one explains the differences.

It might be misleading to refer to a Synoptic Problem.  perhaps we should refer to Critical Synoptic Questions!

BASIC ASSUMPTIONS OF THIS COURSE
Two basic views are held regarding the order and relationship of the Synoptic Gospels.

Matthean Priority.   
This view was supported by the ancient church.  The foundations of this argument were, however, not sound or convincing.  Modern views on Matthean Priority are more convincing.  Those leading in these modern views followed by and large the arguments of Professor William Farmer of Perkins School of Theology, Southern Methodist University, in Dallas.  Factors in support of this view are, 1) that it dispenses with the need for a separate "sayings source," "Q", of Jesus' teachings, and, 2) Papias' supposed contention that Matthew wrote the sayings of Jesus in the Hebrew language, which sayings were translated into the Greek form of our Gospel of Matthew.  There is no reliable evidence of such an original Hebrew source.   Farmer's view, although interesting and challenging, has not been adopted by many contemporary scholars.  This view is commonly known as the "Griesbach" theory.

Markan Priority.  
This view, sometimes called the Lachmann theory, is the one held by most scholars today.  Popularized by B. F. Streeter's view that Mark was the original Gospel source and that Matthew and Luke each used two sources in addition to Mark.   Matthew built into mark's chronology teaching material from a source such as "Q" (either a written or oral source) and material from his personal "notebook," "M".  Luke also used Q and his personal "notebook," L.  Due to the fact that Mark is a dynamic gospel with "rougher" Greek, scholars feel that it should be held as original rather than a reduction of Mathew, which has "smoother" Greek.  This view is sometimes called the "Lachmann" theory.

In this course we will work under the assumption that Mark was the first Gospel written.

We will propose that Matthew adopted Mark's chronological structure and built into his Gospel narrative material from his own sources, identified as "M", and considerable amount of teaching or sayings material known as "Q".  We will notice that Matthew concentrated this teaching/sayings material into five blocks of teaching material to meet the catechetical needs of his community.

Luke, also following Mark's chronological structure, built into this material derived from his own research, known as "L" and some teaching material also from "Q".  Luke does not collect the teaching or sayings material into catechetical blocks as does Matthew.

One should not be over concerned by these scholarly proposals which are interesting and helpful to critical studies of the gospels, but have little to add to the individual worth of the individual gospels.  Each Gospel stands in it's own right upon it's own, merits and the fact that it was included in the New Testament canon.

Students should read the assigned materials in the Syllabus on the Synoptic Problem before progressing on to the lesson.

BASIC HISTORY OF SYNOPTIC STUDIES
Attempts to unravel the "original" gospel source and establish an order for the appearance of the gospels is as old as the church itself.  However, in the modern era of the enlightenment, one needs to pick up this history with the German theologian Gotthold Lessing (c.a. 1778).

See the following references for information on The Synoptic Problem and the History of this topic:<

Gotthold Lessing (c.a. 1778)
Lessing postulated an hypothetical Gospel of the Nazarenes (possibly drawing on the Papias tradition) which was written in Aramaic.  He proposed that three versions of this Aramaic Gospel of the Nazarenes existed.  The Synoptic Gospels are three independent translations of these three hypothetical Aramaic gospels.   The problem with this proposal is that it is based purely on a speculative hypothetical Gospel to the Nazarenes for which we have no evidence at all.

Johannes J. Griesbach (c.a. 1789)
Griesbach, like Lessing, proposed an hypothetical "Apostolic" Gospel or source.  Matthew translated this into Greek.   Luke, influenced by Matthew, did likewise.  Mark finally abbreviated Matthew/Luke into his gospel.  As in the case of Lessing, we have no evidence for this hypothetical Aramaic Apostolic Gospel.

J. G. Eichhorn (c.a. 1794)
Eichhorn adopted Griesbach's hypothetical Apostolic Aramaic Gospel, but enlarged on Griesbach by proposing multiple copies of this original Apostolic Gospel, some of which were revisions of the "original".  Each of our gospel writers used a different Revised Apostolic Aramaic Gospel in his Greek translation.  This theory allowed for the similarity in our three Gospels, and accounted for their differences.   However, as in the previous two views, the weakness lay in the "non existence" of, or lack of evidence for any of these Aramaic Gospels.   Furthermore, this theory does no account for the Greek interdependence of our three Greek Gospels.

Herbert Marsh (c.a. 1801)
Marsh's theory proposed an original Greek Ur-gospel, possibly an Ur-Marcus which began with the baptism of Jesus and ended with his death, burial, and resurrection.   In addition, Marsh postulated a "primitive" sayings source which contained the teachings of Jesus.  Matthew, Luke, and Mark combined these two sources with other material into their three gospels.  This theory accounted for both the content and linguistic similarities in our three Greek Gospels.  The weakness in this theory lay in the hypothetical Ur-gospel for which no evidence is extant.

Friedrich Schleiermacher (c.a. 1832)
Schleiermacher began with at least two original oral sources, a Passion Tradition and a Miracle Tradition.  These were a form of Oral Memorabilia.  The Passion and Miracle traditions were combined into a Greek Ur-Marcus which Matthew combined with an oral sayings tradition (Papias).   Luke then was influenced by Matthew in writing his gospel.  Mark was an independent form of the Ur-Marcus.  The Apocryphal Gospels then used Mark as the basis of their gospels.  The problem with this theory lay in the existence of the hypothetical Ur-Marcus.  The use of the Ur-Marcus was an attempt to explain the linguistic similarities in our three gospels.

Carl Lachmann (c.a. 1835)
Lachmann suggested the existence of an Ur-Gospel and a logia (teaching-sayings) source.  Mark based his Gospel on this Ur-Gospel, incorporating some of the material from the logia source.  Matthew followed with another version of the Ur-Gospel and logia source.  Luke used the Ur-Gospel and Matthew in developing his Gospel.  Lachmann argued that since Mark never deviates from the order set out in both Matthew and Luke, that Mark, therefore, preserves best the order of the original Ur-Gospel.  Lachmann, therefore, suggested that Mark must be the first of the three canonical Gospels.

Heinrich Holtzmann (c.a. 1862)
Holtzmann proposed two primary sources, Alpha (a Narrative Source or Ur-Marcus), and Lambda (a logia sayings source).  Mark, the first of our Gospels, used Alpha as his primary source with some Lambda.  Matthew, the second of our gospels, used Alpha and much of Lambda.  Luke the third of the Gospels combined Alpha and Lambda but differently from Matthew.  Luke was not aware of Matthew.

B. F. Streeter (c.a. 1924)
Streeter proposed what has become known as the Two Source Theory.  The difference in Streeter's two source theory and that of Holtzmann and Lachmann is that the primary source is not an unknown hypothetical source, but the canonical Gospel of Mark.   Streeter, therefore, held that Mark was the first of our Gospels.  Matthew built into Mark sayings material from a source identified as "Q" (quella - source).  Matthew in addition to Mark and Q had material from a Jerusalem source which is known as" M".  Luke, like Matthew combined Mark with Q and other material, "L", of a Caesarean provenance.  In this two source theory, Mark and Q are normally identified as the two primary sources of Matthew and Luke.

Ian A. Fair (c.a.2000)
Fair proposes a multiple source theory similar to that of Streeter.  With Mark being the primary source.  Mark had written his Gospel based on Peter's preaching (See C. H. Dodd). 
Mark was an independent theologian writing for a Roman readership. 
Matthew based his gospel on the primary framework of Mark, building into Mark some independent OT prophetic sayings, some material from a sayings-teaching source (we might refer to this as Q, but this Q may be either a written source, an oral source, or several sayings sources).  Furthermore, Matthew built into his Gospel other material (Streeter's Jerusalem M) which he may have known from personal experience or from personal research.  The basis of this M material may have been either written or oral traditions.
Luke, like Matthew combined Mark's basic narrative with sayings material (oral or written Q), eyewitness information, and material from a Caesarean L source.  This L material may have been a form of proto-Luke.