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This is a good question. A public work on this was made by Bart Ehrman titles Did Jesus Exist. It’s meant to lay audiences but he goes over a lot of the Jesus myth theories and debunks them.
A more academic work is John P Meiers work, A Marginal Jew. In Book 1 he looks at the sources for the historical Jesus, which he differentiates from the Biblical Jesus, or what others have called the Christ of faith.
So the sources for Jesus are the Gospels, Paul, and Josephus. Each source has their issues, but most historians agree that they can just be dismissed, and Meiers really goes over this.
Probably the best single source for evidence that Jesus existed though is Josephus. He was a Roman Historian (who was also Jewish), he wrote relatively shortly after the death of Jesus, and is a primary source for the history of Palestine in the first century. From Josephus we learn the basics. Jesus had a brother named James. Some called him the Messiah. He had a small following. He supposedly performed miracles. He was crucified. And after his death his movement continued.
For Josephus, Jesus is only one of many so called Messiahs and really isn’t special.
One thing to keep in mind is that in the first century Palestine, virtually everyone was illiterate and no one cared about the area. We know this because we have pretty much no sources covering the area besides Josephus. When it comes to one of the most impactful events of Jewish history during that time, the destruction of the Jewish Temple, it is only Josephus who records it. So we are talking about an oral society that had oral traditions as opposed to written traditions. That’s why we lack written records on Jesus because we lack written records about everything during that time.
There's always more that can be said, but you might like to check out these threads on this topic.
What is the evidence for there being a Historical Jesus? Do we always need to rely on the Bible as a source to assert that Jesus was a real person? with an answer from /u/IamMythHunter.
And How much evidence is there for a historical jesus christ besides the bible? from /u/talondearg.