Alvar Ellegard offers a compiliation of questionable, unsupported speculations that are tied together into a single thesis, that Jesus (as the title inferred) was not of the first century AD. The core premise: The Jesus preached by Paul and certain NT writers actually lived in the first century BC and was known as the Teacher of Righteousness, alluded to in the Dead Sea Scrolls. The person responsible for putting Jesus in the first century was the church father Ignatius, who apparently decided this because he thought that was about the time Paul had a vision of Christ.
It is not hard to see, though, that Ellegard has not taken Biblical scholarship seriously. Of attempts to get back to the Aramaic of the Gospels, he has said, "Nothing very substantial has come of these efforts." Scholars of Aramaic like Maurice Casey and Matthew Black would be substantially surprised to hear this from Ellegard, who does not know any Aramaic.
Ellegard offers questionable ideas such as claims of a spiritual resurrection in Paul  (see here) and Paul being a Gnostic. Some 80% of his arguments are the same as those used by Earl Doherty in terms of the reputedly problematic "silence" of the NT epistles concerning the life of Jesus.
Documents are freely and arbitrarily dated to accommodate the thesis. The Gospels and Acts are dismissed as second-century fabrications, while the Shepherd of Hermas is dated before 70 AD. The arguments for the latter are based on less than a half-dozen common vocabulary words.
Ellegard asserts that Essenes lived all over the Roman Empire. What evidence does he have for this highly unorthodox view? He points to a line in the Roman satirist Horace who refers to Roman Jews observing the "thirthieth sabbath" and said that the Essenes used a calendar with numbered Sabbaths. He admits that yes, this isn't much to go on, and there was no evidence other Jews didn't number Sabbaths, but rather than accept this as a lack of validation, we are told we are better of not "shutting our eyes to the possibilities which are simply excluded by our preconceived ideas."
Secular testimony of Tacitus is merely dismissed as repeated hearsay, a claim we have dealt with here.
By itself, these issues are enough for us to decide that Ellegard is not a serious theorist nor a challenge to an informed Christian faith.