Arizal and Ba'al Shem Tov
Q: Please explain reincarnation in the systems of the Arizal and the Ba'al Shem Tov.
A: There are many volumes of the Arizal (Rabbi Isaac Luria) that explain the concepts related to reincarnation. The Arizal discusses when and how reincarnation takes place. He also gives details regarding many soul-roots and how we find them reincarnated in the Bible and afterwards in the time of the Oral Torah, the Sages, and even to the age of the Arizal, himself. He traces the gilgulim from Adam until his own generation and explains that reincarnation is in order to rectify another level of the soul. The Arizal also revealed to people their reincarnation so that they would be able to rectify the blemishes of the previous lifetime.
The way of the Ba'al Shem Tov and Chassidut is awareness of reincarnation, especially by the tzadik ("righteous one"). It is not necessary to reveal this information to every individual. Sometimes knowing one's reincarnation can be detrimental to his personal rectification. It confines a person's mind and doesn't allow him to be open to achieve good in a simple and pure fashion, as he can by being a pure and simple Jew without knowledge of previous lifetimes. That knowledge can narrow one's consciousness as opposed to broadening it.