Our weekly Torah portions (Hebrew: Parashas) serve to cross-reference the Torah and Tanach ("Old Testament") passages with B'rit Chadasha ("New Testament") passages to reveal their seamless continuity, thus revealing God's continuous, ongoing disclosures from Genesis to Revelation. Each week the parashas will be examined in context as we make our way through the Torah during the course of a year. (The first parashah, for example, is Parashat B'resheet/Genesis, which covers the beginning of Genesis to the story of Noah.)
There are 54 parashahs in all, one for each week of the year (including leap years), so that in the course of a year, we read the entire Torah (Genesis to Deuteronomy). During non-leap years, there are 50 weeks, so some of the shorter portions are doubled up. We read the final portion of the Torah right before a holiday called Simchat Torah (Rejoicing in the Torah), which occurs in October, a few weeks after the Feast of Rosh Hashana/Trumpets (which is also the Jewish New Year).
The Haftarah consists of the portions from the Tanach (writings and prophets), and Brit Chadasha readings are from the "New Testament" scriptures all of which correlate to that week's Torah portion. (For our studies we use OT scriptures from Stern's Complete Jewish Bible; and NT scriptures from the AENT.)
It is important to note that on some weeks we read "dual parashahs." Why? The simplied explanation for this is: The five Books of Moshe (Torah) are divided into 54 "readings." Because that is close to the number of weeks in a year, tradition is to read one parashah per week. Obviously with 54 readings, two weeks have to be doubled.
But it's far more complex than that, because the Hebrew year sometimes has 13 months, and so, some years parashahs are read on individual weeks, where the year before, they would be doubled. Furthermore, during the week of Pesach (Passover) regular parashahs are not read, in favor of readings about Passover. Also, regular parashahs are not read during the week of Sukkot (Tabernacles). Nevertheless, all 54 parashahs are read each year, which results in many weeks where parashahs are doubled, to ensure reading them all.