There are some who say Jesus never lived but are relatively few in number. However their ideas are often given credence far beyond their worth .
Here is a useful article look at Tacitus a Roman historian (author of the twelve Caesars) and Flavius Josephus a Jewish historian.
I must admit I nicked this from Tom Holland’s twitter feed. (I do like his books).
I also nicked these quotes from Tacitus;
In the capital, appalling customs & disgraceful practises from every corner of the world cross-pollinate and become fashionable” – .
He never wore the same outfit twice – [on Nero]
So fat was Drusillianus, a slave of Claudius’s who worked as a financial administrator in Spain, that he was nicknamed ‘Rotundus’.
No one in Germany finds vice a laughing matter
More seriously read this article http://www.biblicalarchaeology.org/daily/people-cultures-in-the-bible/jesus-historical-jesus/did-jesus-exist/
Did Jesus Exist? Searching for Evidence Beyond the Bible