A rabbi is not a priest, neither in the Jewish sense of the term nor in the Christian sense of the term. In the Christian sense of the term, a priest is a person with special authority to perform certain sacred rituals. A rabbi, on the other hand, has no more authority to perform rituals than any other adult male member of the Jewish community. In the Jewish sense of the term, a priest (kohein) is a descendant of Aaron, charged with performing various rites in the Temple in connection with religious rituals and sacrifices. Although a kohein can be a rabbi, a rabbi is not required to be a kohein.
A rabbi is simply a teacher, a person sufficiently educated in halakhah (Jewish law) and tradition to instruct the community and to answer questions and resolve disputes regarding halakhah. When a person has completed the necessary course of study, he is given a written document known as a semikhah, which confirms his authority to make such decisions.
When we speak generally of things that were said or decided by "the rabbis" or "the sages", we are speaking of matters that have been generally agreed upon by authoritative Jewish scholars over the centuries. When we speak of rabbinical literature, we speak of the writings of the great rabbis on a wide variety of subjects.
Since the destruction of the Temple, the role of the kohanim has diminished, and rabbis have taken over the spiritual leadership of the Jewish community. In this sense, the rabbi has much the same role as a Protestant minister, ministering to the community, leading community religious services, and dealing with many of the administrative matters related to the synagogue.
However, it is important to note that the rabbi's status as rabbi does not give him any special authority to conduct religious services. Any Jew sufficiently educated to know what he is doing can lead a religious service, and a service led by such a Jew is every bit as valid as a service led by a rabbi. It is not unusual for a community to be without a rabbi, or for Jewish services to be conducted without a rabbi.
A chazzan (cantor) is the person who leads the congregation in prayer. A professional chazzan is generally a person with a well-trained and pleasing voice, because much of the Jewish religious service is sung, but the primary qualifications for the job are good moral character and thorough knowledge of the prayers and melodies. Larger congregations may hire a professional chazzan. In smaller congregations, the rabbi frequently acts as chazzan, but any person can fill the role.
The kohanim are the descendants of Aaron, chosen by God at the time of the incident with the Golden Calf to perform certain sacred work, particularly in connection with the animal sacrifices and the rituals related to the Temple. After the destruction of the Temple, the role of the kohanim diminished significantly in favor of the rabbis; however, we continue to keep track of kohein lineage.
Kohanim are customarily given the first aliyah (i.e., opportunity to recite a blessing over the Torah reading and read from it) on the Sabbath and other days when the Torah is read in public, which is considered an honor. They are also required to recite a special blessing (Numbers 6,24-26) over the congregation in every morning prayer and in additional prayers.
The term "Kohein" is the source of the common Jewish surname "Cohen", but not every Cohen is a Kohein and not every Kohein is named Cohen.
The entire tribe of Levi was set aside to perform certain duties in connection with the Temple. As with the Kohanim, their importance was drastically diminished with the destruction of the Temple, but we continue to keep track of their lineage. Levites are given the second aliyah on the Sabbath (i.e., the second opportunity to recite a blessing over the Torah reading), which is considered an honor.
Chasidic communities are led by a leader with special, mystical power called a "tzaddik" (literally, righteous one). A tzaddik is also called a rebbi, which is sometimes translated "grand rabbi". The position is usually hereditary. A tzaddik has the final word over every decision in a chasid's life.
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