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:
Hebrew dictionary, called "Agron"
translation of the Bible into Arabic with commentary
Halakhic works including responsa
Do a browse subject search under: geonim or geonic literature
For the Responsa (She'elot u-teshuvot) of the Geonim, do a browse subject search under: responsa to 1040
Many of the works by or about the Geonim will be shelved in BM 501.5
Includes the Hebrew texts of the Tanakh, Talmuds, early commentaries, codes, and many responsa. Searching is allowed from anywhere, more features are available (saving, printing, etc.) from the HUC campus or through the Jewish Studies Portal.
Many older rabbinic works are available in PDF form on this site.