What are the origins of the Ashkenazi Jews?

Answer 1

The origins of the Ashkenazi Jews are indigenous Israelite tribes of Canaan in the Middle East. It is also thought that the Ashkenazi Jews likely began settling along the Rhine in Germany.

Answer 2

A relatively small community of Jews, mostly men, came north of the Alps in late Roman times, settling as far west as Paris, but concentrated in the Rhineland. They apparently took converts as wives, and prospered, developing Yiddish language from Hebrew, old French, and lots of German. When the first Crusade was organized in northern France, one of the first things the Crusaders did was slaughter local Jewish communities, driving Jewish refugees east into Poland. The Polish kings of the era encouraged Jewish settlement because it would be good for the economy (it was), and Poland remained a refuge for Jews until the late 17th century. Russia ended up annexing large parts of Poland, gaining a huge Jewish population as a result. In Poland and Russia, Yiddish picked up lots of Slavic loan words. There's plenty of historical and archeological evidence for the history outlined above.

There is a competing theory, very popular in white nationalist and anti-Israeli circles, that Ashkenazic Jews are descended from the Khazars, a Turkic kingdom in western Asia. There is a tiny bit of historical evidence that at least the leadership of the Khazar kingdom converted to Judaism some time in the 8th century. There's ample evidence that Jewish merchants in that era had made their way along the silk road all the way to China, so central Asian kingdoms certainly had at least some contact with Jews. There's no reason to believe that Jewish refugees from Khazaria made up more than a tiny fraction of the Ashkenazi community of later years. The Khazaria hypothesis completely fails to explain why Yiddish is built on German grammar and how it came to incorporate a scattering of loan words from old French. The Khazaria hypothesis also fails to explain why there were so many Jews in the Rhineland at the time of the First Crusade.