At the end of Shacharit, we read from the Torah. It was Moshe Rabbenu who instituted the weekly reading. Seven men are called up to the Torah; the eighth is called up for Maftir and reads the Haftara.
The Torah is divided into 54 weekly portions:
12 in the book of Bereshit
11 in the book of Shmot
10 in the book of Vayikra
10 in the book of Bamidbar
11 in the book of Devarim
Each Shabbat of the year is known by the name of the section of the Torah which belongs to that day. There are more Parshiyot than there are weeks to the year so that on some Shabbatot, the portions must double up. That way we read and study the whole Torah every year. The Book of Bereishit is begun the Shabbat after Shmini Atzeret/Simchat Torah and the entire reading is completed on Simchat Torah of the following year.
Here is a list of Parashat Hashavua Links:
Torah FaxProject GenesisOrthodox Union On Line