The process of descent, and subsequent elevation and ascent through rectification outlines a dynamic concept of spiritual progress and evolution. The Jewish Virtual Library gives the following description:
They maintain that transmigration occurs in all forms of existence, from the Sefirot ("emanations") and the angels to inorganic matter, and is called din benei ḥalof or sod ha-shelaḥ. According to this, everything in the world is constantly changing form, descending to the lowest form and ascending again to the highest. The kabbalists of Safed accepted the doctrine of transmigration into all forms of nature and, through them, this teaching became a widespread popular belief.
Dubrov gives details of the soul’s journey, which parallels the above-described cosmic process at a microcosmic level:
The soul is eternal, a spark of the Divine, or as the prophet Job calls it “a part of G‑d above.” The soul exists before it enters the body and it lives after the body is laid to rest. Though the soul’s place of origin is in the higher worlds, there is something that the soul can achieve in a body that it cannot achieve in the heavenly realms. It has already been explained that the purpose of creation is to make an abode for the Divine in this world. Although higher worlds are glorious in terms of revelation and offer the best reward for a soul after it has achieved its earthly mission, the heavenly realms are not the purpose of creation. It was G‑d’s desire to create a world where His presence would be acutely concealed and darkness and evil would prevail. He charged his children with the task of creating a home in this world, and the soul fulfills that mission by its adherence to Torah and Mitzvot.
Kabbalah explains that the soul is comprised of 613 channels, which parallel the 248 limbs and 365 blood Vessels of the body. These 613 channels attain eternal elevation when all 613 Mitzvot are fulfilled by a soul in its earthly descent.
Usually a soul does not manage to fulfill all the commandments in one descent, and the Arizal writes that every soul must be repeatedly reincarnated until it has fulfilled all 613 Mitzvot in thought, speech, and action. In the previous chapter, the notion of purification through Gehinom was introduced. (Dubrov)
Furthermore, Dubrov notes that:
Here the soul is cleansed in order to be elevated to the Garden of Eden. How is this concept reconciled with the possibility of reincarnation and a return to our world? The Kabbalists explain that when a soul returns to this world, the part of the soul that was elevated by its Torah learning and Mitzvah performance is not reincarnated, rather it is only the other parts of the soul that were not affected by the first incarnation that return. The possibility of a soul being divided and part of a soul being reincarnated is discussed at length in Kabbalah. (Dubrov)
The Baal Shem Tov in his Instruction in Intercourse with God (Of the Holy Sparks and their Redemption), considers that humans are participants in the scheme of cosmic renewal:
"The Holy Sparks that fell when God built and destroyed the worlds, man shall raise and purify upward from stone to plant, from plant to animal, from animal to speaking being -- purify the Holy Sparks that are imprisoned in the world of Shells . . . And who, with the good strength of his spirit, is able to raise the Holy Spark from stone to plant, from plant to animal, from animal to speaking being, leads it into freedom; and no setting free of captives is greater than this. It is as when a king's son is rescued from captivity and brought to his father." (Buber, 89)
(Instructions on Intercourse with God, p. 188 in Hasidism and Modern Man by Martin Buber.)
The body-soul relation in this process involves a complex explanation of the human constitution. Jacobs outlines a basic dualistic concept:
Rabbi Schneur Zalman explains in the Tanya that every Jew is composite of two distinct souls. The first soul is the Nefesh HaBehamit which animates the body. This soul is complete with an infrastructure of soul powers ranging from pleasure and will to intellect and emotions. Common to all the soul powers of the Nefesh HaBehamit is that they all wish to fulfill the base needs, passions, and desires of the body. Essentially the Nefesh HaBehamit is self-centered.From it stems the negative character traits, such as anger, apathy, and arrogance.
The second soul is the Nefesh Elokit. This soul is described by Job as “a part of G‑d,” and exists both before its descent into the body and after the ascent from the body. The Nefesh Elokit in itself is not in need of rectification; rather its descent into this world is to refine the base and the animalistic nature of this material world. (Jacobs)
Brandwein explains the more complex fivefold nature of the soul:
The Midrash states that the soul has five names:
Nefesh (soul of vitality),
Neshamah (breath of life),
Chaya (living one), and
Yechidah (singular one). (Brandwein)
He adds that:
According to the Zohar, the four higher levels of the soul usually enter a person during his lifetime in Ibur: First, a person receives nefesh when he or she is born; then, when they merit it, they receive ruach; when they merit it, they receive neshamah; when they merit it, they receive chayah. The higher the level, the rarer its occurrence. Very few have ever merited to neshamah, let alone chayah. Nobody has ever received the highest level, yechidah. Adam would have received it had he not sinned. (Brandwein)
Moreover, one can find a classic esoteric microsmic-macrocosmic correspondence in this system. Dubrov notes that:
Kabbalah explains that these five names of the soul correspond to the level of soul in each of the worlds. Nefesh corresponds to the soul in the realm of Assiyah, Ruach in Yetzirah, Neshamah in Beriah, and Chaya in Atzilut, while Yechidah represents the quintessential point of the soul (Etzem HaNeshamah) which is rooted in the Or Ein Sof. Hassidism teaches that the Nefesh resides in the blood, Ruach in the heart, Neshamah in the brain. Chayah and Yechidah are transcendent of the body, not enclothing themselves in any particular limb. The Kabbalists explain that through successive incarnations, all levels of the soul are elevated. (Dubrov)
Jacobs gives a succinct summary of the basic types of reincarnation:
In the kabbalistic literature three types of reincarnation are mentioned:
1. gilgul, transmigration proper, in which a soul that had previously inhabited one body is sent back to earth to inhabit another body.
2. ibbur, “impregnation,” in which a soul descends from heaven in order to assist another soul in the body.
3. dybbuk, a generally late concept, in which a guilt‑laden soul pursued by devils enters a human body in order to find rest and has to be exorcised. (Jacobs)
Brandwein gives the following explanation for Ibbur Neshamot:
It involves receiving a new (higher) soul sometime during one's lifetime. That is, a new soul comes into a person's heart while he is still alive. The reason this is called Ibur, gestation or pregnancy, is because this person becomes "pregnant" with this new soul while he is still alive. This phenomenon is the deeper explanation behind certain people going through drastic changes in their lives. They either undergo a change of mind about certain things or change their lifestyle, and thereby ascend to the next spiritual level. This is also included under the general heading of gilgul-incarnation because they are now hosting a new soul [or an aspect of their own soul or a higher soul of which they are a part] in order to be a vehicle for that soul's rectification. This is what occurs when a person is ready to advance in his soul evolution. This is why the soul has five names, each higher than the other, nefesh, ruach, neshamah, chayah and yechidah. (Brandwein)
The Jewish Encyclopedia offers the following explanation of Dybbuk:
This belief assumes that there are souls which are condemned to wander for a time in this world, where they are tormented by evil spirits which watch and accompany them everywhere. To escape their tormentors such souls sometimes take refuge in the bodies of living pious men and women, over whom the evil spirits have no power. The person to whom such a soul clings endures great suffering and loses his own individuality; he acts as though he were quite another man, and loses all moral sense. He can be cured only by a miracle-working rabbi ("ba'al shem") who is able to cast out the soul from his body by exorcisms and amulets. The usual exorcism in such cases consisted in the rabbi's reciting, in the presence of ten men (See Minyan), the 91st Psalm, and adjuring the soul in the name of God to leave the body of the afflicted one. In case of refusal on the part of the soul to yield to this simple injunction, the ban and the blowing of the shofar are resorted to. In order that it may cause the least possible amount of damage to the body, the soul is always directed to pass out through the small toe. (Jewish Encyclopedia)
Yaakov Astor . (Reincarnation and Jewish Tradition) Soul Searching, Targum Press
Rabbi Avraham Brandwein (Gilgul Neshamot - Reincarnation of Souls) (Transl. Avraham Sutton)
Martin Buber, Hasidism and Modern Man, 1958
Nissan Dovid Dubrov (The Soul and the Afterlife)
Rabbi Louis Jacobs (Is there a Jewish Afterlife?)
Jewish Encyclopedia (Gilgul Neshamoth)
Jewish Virtual Library (Gilgul)
Aryeh Kaplan. Sefer Yetzireh – The Book of Creation. Weiser, 1990.