Gilgul neshamot, the rolling or cycling of souls, is the Jewish doctrine of reincarnation. It is not found in the Hebrew Bible or in the Talmud, and medieval Jewish rationalism rejected it: Saadia Gaon, in Beliefs and Opinions, dismissed it explicitly as a notion imported from outside. Its entry into Jewish thought is by way of Kabbalah, first attested in the twelfth-century Sefer ha-Bahir, developed in the Zohar, and made central by the Lurianic school of sixteenth-century Safed.
In the Lurianic system, set out in Hayyim Vital's Sha'ar ha-Gilgulim, souls return in order to complete commandments left undone, to repair damage done in an earlier life, or to be matched to circumstances that permit a specific rectification. A related mechanism, ibbur (impregnation), has an additional soul temporarily join a living person to accomplish a particular task or to assist them. Hasidism absorbed the whole doctrine, and it lies behind the popular figure of the dybbuk, a soul that has failed to move on and attaches itself to the living.
Its standing in Judaism has never been that of a required belief. It is widely accepted in Hasidic and kabbalistically inclined Orthodox circles, treated as an optional or non-operative view in much of Modern Orthodoxy, and generally not held in Reform, Conservative or Reconstructionist Judaism. Comparisons with Indian doctrines of rebirth are frequently drawn but the differences are substantial: gilgul is not governed by a general law of moral causation of the kind karma describes, is often held to be limited in number, and does not displace the resurrection of the dead as the tradition's ultimate horizon.