The historicity of Jesus deals with whether or not Jesus actually existed and may involve different areas of study. Some have sought to simply prove that Jesus existed, doing so from extra-biblical literature (writings
outside the Bible). Others seek to prove the authenticity of his miracles, sayings, and teachings, while some focus on proving his resurrection, or discrediting the assertions that things written in the Gospels were untrue.
Necessarily related to this is the historicity of the New Testament. If the NT is not reliable, then it cannot be a dependable source for the study of Jesus.
The Jesus myth
The Jesus-myth is "the idea that Jesus did not even exist, much less conduct a ministry as described in the New Testament. . . Support for the 'Jesus-myth' comes not from historians, but usually from writers operating far out of their
field. . . In spite of the fact that relevant scholarly consenus is unanimous that the 'Jesus-myth' is incorrect, it continues to be promulgated on a popular level as though it were absolutely proven." J. P. Holding, www.tektonics.org/jesusexist/jesusexisthub.html
Arguments for the Jesus myth
Adherents to the Jesus myth often argue that Jesus is the product of pagan myths of rising and dying gods. Doctrines such as the virgin birth, crucifixion, and resurrection were borrowed off earlier myths of pagan deities such as Osirus, Mithra, and Attis.
In addition to this, it is alleged that there is a lack of historical evidence for the existence of Jesus.
Almost no serious scholar holds to the first argument, which states that Jesus was borrowed off pagan myths. Most of these alleged parallels postdate Christianity and thus show a reversed dependency. These parallels are also the product of reading specifically
Christian theology into it. Mithra for example, was born of a rock. Reading Christian terminology into it makes it sound as if Mithra was born of a virgin. Samuel Sandmel has referred to this as "Parallelomania." 
There is also no lack of historical evidence for the existence Jesus. In their book The Case for the Resurrection of Jesus, Gary Habermas and Mike Licona list more than forty sources which mention Jesus within 150
years within His life.
- R. T. France, The Evidence for Jesus (1986)
- Gerd Theissen and Annette Merz, The Historical Jesus: A Comprehensive Guide (1996)
- Robert Van Voorst, Jesus Outside the New Testament (2000)
- Gary Habermas, The Historical Jesus: Ancient Evidence for the Life of Christ (1996)
- Craig Blomberg, The Historical Reliability of the Gospels (1987)
- Gregory Boyd and Paul Rhodes Eddy, The Jesus Legend: A Case for the Historical Reliability of the Synoptic Jesus Tradition (2007)
- James Patrick Holding, Shattering the Christ Myth: Did Jesus Not Exist? (2008)
- Arthur Drews, The Christ Myth (1998)
- Earl Doherty, The Jesus Puzzle: Did Christianity Begin with a Mythical Christ? (1999)
- Harold Liedner, The Fabrication of the Christ Myth (2000)
- Thomas Thompson, The Messiah Myth: The Near Eastern Roots of Jesus and David (2005)
- George Wells, The Historical Evidence for Jesus (1988); Who Was Jesus? (1989); The Jesus Legend (1993); The Jesus Myth (1998); Can We Trust the New Testament? (2005)
“Do you believe in the existence of Socrates? Alexander the Great? Julius Caesar? If historicity is established by written records in multiple copies that date originally from near contemporaneous sources, there is far more proof for Christ’s
existence than for any of theirs.” Dinesh D’Souza, What’s So Great About Christianity, p. 296
"I have taken it for granted that Jesus of Nazareth existed. Some writers feel a need to justify this assumption at length against people who try from time to time to deny it. It would be easier, frankly, to believe that Tiberius Caesar, Jesus'
contemporary, was a figment of the imagination than to believe that there never was such a person as Jesus." N. T. Wright, Jesus and the Victory of God