Reincarnation
Reincarnation is the doctrine according to which the soul, after physical death, is reborn in a new body. Present in Hinduism, Buddhism, Jainism, Sikhism as part of the cosmology of samsara (cycle of birth and death). In the West it returned through Spiritism (Kardec, 1857) and Theosophy. Mainstream Christianity rejected the doctrine at the Council of Constantinople in 553.
Eastern vs Western view
In Hinduism/Buddhism, reincarnation is something to be escaped from (via moksha or nirvana). In Spiritism, reincarnation is positive: opportunity for moral evolution.