Who Wrote the Gospels
     I could keep this brief by simply saying we don't know, but I'll elaborate a bit.
     Mark is considered to be the earliest of the gospels. Written around 70 A.D., immediately before or immediately after the destruction of Jerusalem, it makes one wonder as to the accuracy of a story recounted nearly 40 years after the death of Jesus.  Mark also displays a very poor knowledge of Palestinian geography, and was most likely written in Rome.
     According to Reginald H. Fuller, professor Emeritus of the Virginia Theological Seminary, the earliest writings of Mark contain no story of Jesus' appearance after his death. The myth seems to have been added later.
     The writer of Mark might have been named Mark, but the one refered to by Peter as " Marcus my son " in  1 Peter 5:13
     Luke was written, we think, around 85 A.D., some 50 years after the fact. It's author is unknown, but his poor knowledge of Palestine indicates he was never there, making it certain that Luke didn't write it.
     Matthew was written around 90 A.D., and the author exibits a theological outlook, command of Greek language, and rabbinic training that indicates a second generation Christian Jew. This definitely excludes Matthew as it's author.
     John was written between 100 and 150 A.D.  It's author is, like the other three, unknown, but it's age makes it apparent that John didn't write it.