The Muslim conquest destroyed the Persian Sasanid Empire that had ruled Persia and Babylonia. Under the Persians a very important Jewish center had existed. The Babylonian Talmud is a witness for its importance. The Muslim conquest opened a new area in the Jewish history in Babylonia, the Gaonate period. The most important Gaon was Saadia Gaon, and we shall discuss his importance. In this lesson we shall study the history of the yeshivot, the history of the exilarch, the rivalry between Palestine and Babylonia, the Karaite movement that was created at that time, and the cultural influence of Islam on Judaism.