The Torah is divided into 54 sections called parshiyot and one parshah (singular) is read each week throughout the year (two occasionally). Reading the weekly Torah portion is a hallmark of the learned Jew as new insights emerge each time one engages in the pursuit of Torah. The cyclical nature of the parshiyot reflects Judaism’s connection to time and season. In the synagogue service, the weekly parshah is followed by a passage from the prophets, which is referred to as a haftarah (haftarot, plural). Contrary to common misconception, “haftarah” does not mean “half-Torah.” The word comes from the Hebrew root Fei-Teit-Reish and means “concluding portion”. Usually, the haftarah portion is no longer than one chapter, and has some relation to the Torah portion of the week.
The Torah and haftarah readings are performed with great ceremony: the Torah is paraded around the room before it is brought to rest on the bimah (podium). The reading is divided up into portions, and various members of the congregation have the honor of reciting a blessing over a portion of the reading. This honor is referred to as an aliyah (aliyot, plural; literally, ascension).
To access the most comprehensive, non-denominational weekly Torah and Haftarah portion go to Hebrew Calendar: http://www.hebcal.com/sedrot/. Below is a table of the weekly parshiyot in the order in which they are read:
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