Rabbis teach Jewish law and traditions. Congregations hire rabbis as leaders, both to lead services (although any knowledgeable adult Jew can lead services) and to act as spokesmen for their communities. Rabbis make decisions about matters of Jewish law, leading Jewish courts that oversee such issues as divorce and conversion to Judaism (sometimes, Jewish courts judge other kinds of civil cases where the law allows binding arbitration).
Each community has its own rabbi/rabbis. There's no one central leader today.
Judaism is not a centralised religion and does not have a person who's the equivalent to the Pope. The title Rabbi means teacher and today Rabbis have a number of roles in Jewish life.
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No. The functions of a Rabbi within Judaism are different than the functions of a Minister in Christianity.
A Rabbi or a Cantor (or anyone for that matter) can interpret and teach the laws of Judaism.
The answer that you're looking for is Judaism, but actually, the person who leads the prayers in Judaism is not required to be an ordained Rabbi. Rather, they need a working familiarity with the prayers, with any relevant melodies, and with relevant Jewish laws. See also:Prayer in Judaism