One of the oldest - and for a long time the largest - Jewish communities in the world is the Jewish community of Babylon in modern day Iraq. Jews lived in Babylon continuously for over 2.500 including a long period where they had a Jewish autonomous state led by their own Jewish King.
Babylon was also a center of Jewish scholarship most notable for the Babylonian Talmud, the central work of Judaism that was composed there in the Fifth Century.
A fascinating overview of the history of the Jewish community of Babylon.