Last week's parsha was about Noach and the flood (mabul). After the mabul, Noach's family grew, and the people spread all over the world.
Before the parsha ended, the Torah traced the descendants of Noach's three sons for ten generations until Avrom, our first Patriarch, was born.
This week's parsha is called Lech-Lecha. Lech means, "go", because here G-d is telling Avrom to leave his father's house and land with all its idolatry, and go to a land that G-d will show him. Rashi says "lecha" means for "your" benefit, because G-d is saying that He will make Avrom into a great nation, wealthy, and famous.
In the first aliyah Avrom goes ("lech") and enters the land of Canaan where he traverses up and down, and back and forth in the land. In the Midrash it says that according to Halacha, one way to acquire land is to pace it off, and that is what Avrom was doing, acquiring Eretz Yisroel for the Jewish people.
The second aliyah has Avrom in the land of Canaan with a terrible famine in the land. This is the worst famine the world had ever known, and it only affects the land of Canaan, and it started as soon as Avrom got there. This was right after G-d promised Avrom all sorts of blessing and told him to move to Canaan. As a result, this was one of Avrom's trials, to see if he would complain against G-d. But he didn't.
Avrom goes down to Egypt because he heard that food was abundant there, but his wife, Sarai, was so beautiful that the Egyptians took her captive to marry Pharaoh. But she was a Tzadekas (righteous woman), and prayed to G-d, and He struck the Egyptians with boils. She was released unharmed and given many gifts that made them rich. This paralleled what would happen to the Jewish people in the future: The Jewish people would later descend to Egypt, also because of a famine, in Yakov avinu's time. The Jewish people would then be enslaved by the Egyptians, but the Jewish women would remain modest in an immoral land. The Egyptians will be struck with plagues, and the Jewish people would be released with riches.
In the preceding aliyah, when Sarai and Avrom were released from Egypt with riches, Avrom's nephew Lot was with them and he also became rich because of his association with Avrom. In this, the third aliyah, they return to Canaan, and find it difficult for their two large herds of cattle to get along together, near each other. Lot departs and goes to the vicinity of the cities of Sodom and Amorrah.
When Lot separates from Avrom, G-d speaks to Avrom and blesses him that his descendants shall be as numerous and uncountable as the dust of the earth.
In the fourth aliyah there is a war between several kingdoms including Sodom, and Avrom's nephew Lot is taken captive. Avrom pursues after them and miraculously rescues Lot.
In the fifth aliyah Avrom discusses his childlessness with G-d. He says that G-d promises to make him wealthy, but Avrom says what's the point of all that wealth if he has no son to inherit it.
In the sixth aliyah G-d tells Avrom that his descendants, the Jewish people, will be exiled in a strange land under bondage for 400 years.
Also in this aliyah, Hagar, Sarai's handmaid becomes a second wife to Avrom, and she bears him a son named Yishmael. (Hagar was Pharaoh's daughter. Upon seeing the miracles for Sarai in Egypt, Pharaoh said: "better she should be Sarai's handmaid then a princess in another house.")
At the very end of the aliyah, G-d adds the letter "Hay" to Avrom's name, making it Avrohom.
In the seventh aliyah G-d makes a covenant with Avrohom and his descendants after him: that all males should be circumcised on the eighth day after birth. Sarai's name becomes Sarah in this aliyah.
Avrohom is circumcised, and also, all the males of his household. Avrohom is 99 years when his bris takes place, and Yishmael is 13 years old when his bris takes place.