The geonim were the heads of two Talmud academies in Babylonia (in Sura and Pumbedita) from the late 500's until the early 11th century. It was their role to teach and interpret the Talmud and to formulate legal decisions based on the Talmud.
The Jewish Encyclopedia has a chart of the geonim at Sura and Pumbedita.
One of the best known was Saadia ben Joseph (also known as Saadia ha-Gaon) who was the Gaon of Sura from 928 until his death in 942. He was a prolific author whose works include:
For the Responsa (She'elot u-teshuvot) of the Geonim, do a browse subject search under: responsa to 1040Finding texts on the shelf
Many of the works by or about the Geonim will be shelved in BM 501.5Finding Talmud online
Bar Ilan Responsa Project
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