Chumash
The first five books of the Hebrew Bible or Old Testament are known by several names including: the Five Books of Moses, the Pentateuch in the Greek and simply the Torah. In most English Bibles and in particular translations designed for the Christian Bible the various books of the complete Hebrew Bible are broken down into chapter and verse for easy reading and grouping of stories. However, the Jews do not follow this particular breakdown in the Five Books of Moses, preferring instead a different breakdown called Parshas. Chumash means "five" and The Chumash usually refers to editions of the Torah with Parshas and Haftorah and various commentary.
The Parshas are designed to break the five books into weekly readings so that the entire set of books can be read completely in the course of one year. Additionally, the Parshas present the stories of the Torah not in a strict chronological sense as the more familiar chapter and verse, but more on ideas or series of events, though chronologically still the same. For example, one Parsha that concerns the death of Sarah (the Patriarch Abraham's wife) is called Chaye Sarah - "The Life of Sarah." Though this portion begins with the statement that she died - the name highlights her life.
The Parshas are also connected to other sections of the Hebrew Bible in weekly readings. For example, the opening of the book of Genesis is called Beresheit - "In the Beginning," and contains the story of the creation. This portion is read in conjunction with passages from the Prophet Isaiah where he speaks of how God created the world. These extra readings are called the Haftorah.
Below are some links to sites listing the Parsha names with corresponding chapter and verse along with the Haftorah portion. You will notice that the Parshas often begin and end in the middle of chapters.
Though the Torah Portions don't change, when they are read during the year does change as the Jewish year is lunar. Jews around the world read and study the Parsha each Sabbath beginning the Sabbath following Simcha Torah - the holiday that celebrates the reading of the last portion for the year. That holiday falls on different dates each year due to the lunar calculation. When visiting any of the links below you will often find Parsha reading dates for various years (often designated by the Hebrew year).