The Griesbach Hypothesis
According to the Griebach Hypothesis, Matthew was the first gospel to be written, and Luke used Matthew as a source. Subsequently, Mark used both Matthew and Luke. This hypothesis was very popular for some time, but most scholars today do not think that it correctly accounts for the literary relationship between the Synoptic Gospels.
The Two-Source and Four-Source Hypotheses
The Two-Source Hypothesis holds that Matthew and Luke independently used Mark and a hypothetical sayings document called "Q" as sources. The Four-Source Hypothesis adds two more sources: "M," which is a special source used by Matthew, and "L," which is a special source used by Luke. Most scholars today find these hypotheses to be the best available explanations of the literary relationship between the Synoptics.
L
Mk
Lk
Markan Priority Without Q
This is a hypothesis that has recently re-entered into scholarly debate. According to this hypothesis, Mark was written first, Matthew used Mark, and Luke used Matthew and Mark. One major question with regard to this theory of the literary relationship between the gospels has to do with the amount of authorial/editorial creativity that we will attribute to Luke. In other words, if Luke used Matthew, then he must have reordered a great deal of Matthew's material, including material from the Sermon on the Mount.
