Shalom and thank you for your question. You wish to understand what is the place of reincarnation in Judaism. To understand this, we must first define what Judaism is, and in what Jews believe.
If you ask several Jewish people from different places and walks of life, you will get different answers, depending on the background and outlook of the person you are asking. This is simply because many people have not received sufficient education. The Jewish religion is the only one out of the major Western religions, and perhaps at all, that was given to an entire nation rather than a single prophet or teacher. This took place at Mount Sinai, several weeks after the Jewish people had escaped slavery in Egypt and fled with their teacher and leader Moses into the desert after the miraculous crossing of the Red Sea. They encamped at the foot of the mountain, and G-d revealed Himself as a voice amid thunder and lightning, a voice that had no echo, because it penetrated everything. The entire nation heard and saw this revelation. G-d gave over the first two of the Ten Commandments, and the rest G-d gave over to Moses, who told the people. The Ten Commandments however, are only like chapter headings of the Torah. G-d taught the entire Torah to Moses, who was on the mountain for forty days and forty nights, and thereafter Moses taught it to the nation. It was then handed down through the generations. Practicing Jews world over have received this tradition and handed it down to the next generation.
What IS this Torah that was handed down? It comprises the Five Books of Moses (Chumash) the writings of the Prophets, of King Solomon, the scroll of Esther, and more. All of that is called the Written Law. Along with the Written came the Oral Law. This was also received and handed down. In later generations the Oral Law, comprising Midrash and Talmud and more, had to be written down so that it would not get lost due to the Jews having been exiled from the Holy Land and dispersed among the nations. What is the Oral Law and why do we need it? I will give you an example. In Exodus 35:3 it states “Do not kindle a fire in your dwelling places on the Sabbath day.” Some people who deny the holy origins of the Oral Law take this as it might be understood literally, to mean that one should sit in the dark on the Sabbath and eat cold food. The Code of Jewish Law, derived from the Talmud, instructs us to make sure that our homes are well lit on the Sabbath so that we should not stumble in the dark and we should maintain harmony in the home. We kindle the lights – these days that means turning on the light switch – before the Sabbath and leave them on for the Sabbath. Of course all this refers to the emotional aspect as well. The Shelah haKadosh, an authentic Torah commentator, (authentic commentaries are based on the Thirteen Principles of Torah exegesis that were also handed down at Sinai) explains that this means that we should be extra careful not to kindle the fire of conflict in our homes on the Sabbath, which is supposed to be a spiritual day that elevates mundane weekdays. All of this would not be understood without the Oral Law. There is a third aspect of Judaism that was also handed down to Moses on Sinai, and that is the esoteric, or hidden, dimension of Torah, called Kabbala. Since Kabbala was only handed down to very few and select people in earlier generations, there is a lot of confusion regarding its origins. It is equally a part of Torah (which means teaching) just as are the Written Law and the Oral Law.
Rabbi Shimon bar Yochai composed the Zohar, which eventually got lost and became rediscovered. In every generation however, there were select scholars who studied Zohar and handed it down. When the book of Zohar was rediscovered certain scholars well versed in Kabbalah were able to ascertain that it was genuine. Some people were suspicious of this. In any case, as I said, the knowledge of this inner dimension of Torah was handed down through the generations, albeit to only a limited number of people, just as the knowledge and study of the Written Law and the Oral Law were handed down. Just as the Oral Law helps us understand the Written Law, the Kabbalah helps us understand it all. The topic of reincarnation is a good example of this. Yes, Judaism believes in reincarnation, and Rabbi Isaac Luriah did not make it up, he merely taught the secrets of Kabbalah to certain scholars of his generation. These secrets had been handed down from previous generations dating back to the Giving of the Torah at Mount Sinai.
In the eighteenth century Rabbi Yisrael Baal Shem Tov, a holy and righteous Jew who lived in the area of the Carpathian mountains, began the Chassidic movement. Chassidic teachings present the inner dimensions of Torah, Kabbalistic wisdom, and make it accessible to a wider range of people than in earlier generations. This is because the world has changed and continues to change as we work our way towards a world that will be rectified and we will merit the Messianic era. A Chassidic story will illustrate how the concept of reincarnation can complete the picture of Written Law and Oral Law, and inspire us to be the best people we can.
In the times when there were Jewish kings before the Jews were exiled from the Holy Land, there was a King called Menasseh (Menashe). He unfortunately succumbed to what was then the widespread urge to worship idols, and unfortunately influenced the people to do the same. Eventually after certain dramatic events he repented. Many many generations later in Europe, a Jew who was – I think – an artist, arose one night and entered a church, smashing and destroying all the graven images and representations of Christianity which were there. The local authorities caught him and took him to trial. He was hanged. His poor wife came to the members of the Jewish community who were in charge of charity and requested a stipend, since she was now a widow. There was an argument about whether or not the community was obligated to support her, since what her husband did could be considered suicide. The case was brought before a great Chassidic Rabbi, who began to contemplate it according to Jewish law. This Rabbi was visited by a soul from the World of Truth. The soul belonged to King Menashe, who explained to the Rabbi that he – King Menashe – had been reincarnated as that Jewish artist who destroyed the graven images, in order to rectify his sin of worshipping idols and causing others to do so. By destroying the graven images at the cost of his own life, his soul became rectified. The Chassidic Rabbi was then able to ensure that the widow would receive her stipend from the community. There are so many lessons from this story. One important one is that when we take reincarnation into account, we see that what we know of in life is very limited. G-d is the Creator and has reasons for everything.
We hope that this has been helpful!