Hai ben Sherira (Hebrew: האיי בר שרירא), better known as Hai Gaon (Hebrew: האיי גאון), was a medieval Jewish theologian, rabbi and scholar who served as Gaon of the Talmudic academy of Pumbedita during the early 11th century. He was born in 939 and died on March 28, 1038. He received his Talmudic education from his father, Sherira ben Hanina, and in early life acted as his assistant in teaching. In his forty-fourth year he became associated with his father as "av bet din", and with him delivered many joint decisions. According to Sefer HaKabbalah of Rabbi Abraham ben David (Ravad), he was the last of the Geonim.

As a consequence of the calumnies of their antagonists Hai and his father were imprisoned together and their property was confiscated by the Abbasid caliph al-Qadir in 997. The imprisonment was brief, but shortly thereafter (in 998) the aged and infirm Sherira appointed his son to the position of gaon. Hai's installation was greeted with great enthusiasm by the Jewish population. An old tradition says that on the Sabbath after Sherira's death, at the end of the reading of the weekly lesson, the passage in which Moses asks for an able follower was read in honor of Hai. Thereupon, as haftarah, the story of Solomon's accession to the throne was read, the last verse being modified as follows: "And Hai sat on the throne of Sherira his father, and his government was firmly established." Hai remained gaon until his death in 1038. He was celebrated by the Spanish poet Solomon ibn Gabirol and by Samuel ibn Naghrillah.

Hai ben Sherira's chief claim to recognition rests on his numerous responsa, in which he gives decisions affecting the social and religious life of the Diaspora. Questions reached him from Germany, France, Iberia, Anatolia, the Maghreb, and even India and Ethiopia. His responsa, more than 800 in number, deal with civil law, especially laws concerning women, with ritual, holidays, and so on. Many of them contain explanations of certain halakhot, aggadot, and Talmudic matters. In halakhic decisions he quotes the Jerusalem Talmud, but without ascribing any authority to it. Many of his responsa may have been written in Arabic; only a few of them have been preserved.

Hai ben Sherira codified various branches of Talmudic law. His works include:

These three treatises were published together (Venice, 1604); later editions also contain commentaries by Eleazar ben Aryeh (Vienna, 1800) and by Hananiah Isaac Michael Aryeh (Salonica, 1814). Another anonymous translation of them exists in manuscript under the title "Dinei Mamonot".

According to Rabbi David Azulai, Hai also wrote in Arabic Sha'arei Shevu'ot, a treatise on oaths. According to another Hebrew source, the original title was Kitab al-Aiman. This treatise was twice anonymously translated into Hebrew: (1) Mishpeṭe Shebu'ot (Venice, 1602; Altona, 1782); (2) Sefer Mehubbar be-Kotzer Min ha-Dinim be-Bi'ur Kelalim we-'liqarim be-Helqe Hiyyub la-Shebu'ah Sha'arei Shevu'ot was metrically arranged by an anonymous writer, probably of the 13th century, under the title Sha'arei Dinei Mamonot ve-Sha'arei Shevu'ot, and by Levi ben Jacob Alkalai.

Hai's treatise on boundary litigations, "Metzranut", is known only through quotations.

Hilkot Tefillin, Siddur Tefillah and Metibot are also quoted as his.