Geonim גאונים
The heads of the Babylonian academies for four and a half centuries — the highest authority of the whole diaspora.
The title gaon is short for «head of the academy, the pride of Yaakov». The era begins around 4349, after the savoraim, and lasts to the mid-eleventh century. Geonim headed Sura and Pumbedita, alongside the exilarch, a descendant of David's house who represented the Jews before the caliph.
Their chief instrument was the responsum. Questions came from Spain, North Africa, Italy and Egypt, and their answers effectively turned the Talmud into working law across the Jewish world. Thousands of such letters survive.
They also created new genres: Rav Amram Gaon compiled the first prayer book; Rav Saadya Gaon translated the Tanakh into Arabic, wrote a work of philosophy, a grammar and a siddur, and led the fight against the Karaites. The Epistle of Rav Sherira Gaon is the first systematic account of the chain of transmission.