גלגול הנשמות, Plural: גלגולים Gilgulim) is a concept of reincarnation or "transmigration of souls"[1] in Kabbalistic esoteric mysticism.
The esoteric explanations of gilgul were articulated in Jewish mysticism by Isaac Luria in the 16th century, as part of the metaphysical purpose of Creation.
Rabbis who believed in the idea of reincarnation include, from Medieval times, the mystical leaders Nahmanides and Bahya ben Asher; from the 16th-century Levi ibn Habib, and from the mystical school of Safed, Solomon Alkabetz, Isaac Luria, and his exponent Hayyim ben Joseph Vital; and from the 18th-century: the founder of Hasidic Judaism, the Baal Shem Tov, later Hasidic Masters, and the Lithuanian Jewish Orthodox leader and Kabbalist the Vilna Gaon; and - amongst others - from the 19th/20th-century: Yosef Hayyim, author of the Ben Ish Hai.
[3] In this context, Isaac Luria taught new explanations of the process of gilgul and identification of the reincarnations of historic Jewish figures, which Hayyim ben Joseph Vital compiled in his Shaar HaGilgulim.
[4] Historian Nathaniel Deutsch mentioned a widely reported anecdote as a modern example of the gilgul belief.
"The story goes that a 20-pound carp about to be slaughtered and made into gefilte fish for Sabbath dinner began speaking in Hebrew, shouting apocalyptic warnings and claiming to be the troubled soul of a revered community elder who recently died.