Rabbi Yitzchak ben Yaakov Alfasi, the Rif, was born in 4773 (1013) in Qal'at Hammad, the Qal'at Bani Hammad in present-day Algeria, according to most historians; older sources place it near Fez. He studied at the yeshiva of Kairouan, in Tunisia, under Rabbeinu Chananel and Rav Nissim Gaon, the leading authorities of the age.

Around 1045 he moved to Fez, from which he took the name Alfasi. The Jewish community there supported him and his family so that he could devote himself to his work, and founded a yeshiva in his honour that drew students from all over Morocco. He remained there for some forty years.

In 1088, at the age of seventy-five, he was denounced to the authorities and fled to Al-Andalus. In 1089 he became head of the yeshiva of Lucena. His students included Rabbi Yosef ibn Migash and Rabbi Yehudah HaLevi, author of the Kuzari. On his deathbed he named as his successor not his own son but his student Rabbi Yosef ibn Migash.

His main work, Sefer HaHalachot (Hilchot Rav Alfas), condenses the Babylonian Talmud to its halachically relevant material across twenty-four tractates. Known as the "Talmud Katan", the little Talmud, it is printed in editions of the Talmud. The Rambam wrote that it "has superseded all the geonic codes". Together with the Rambam and the Rosh, the Rif is one of the three pillars on which Rabbi Yosef Karo based the Shulchan Aruch. He also left hundreds of responsa in Hebrew and Arabic.

He passed away on 10 Iyar 4863 (1103), at the age of ninety, in Lucena. The opening lines of a lament composed for him by Rabbi Moshe ibn Ezra were engraved on his tombstone.