Last week's parsha was Lech-Lecha, and at the very end of it, G-d gave Avrohom Avinu the commandment of circumcision, and Avrohom and his household were circumcised.
This parsha, and the first aliyah, begins on the third day after Avrohom's circumcision, when pain from surgery is at its worst, and G-d is visiting the sick by appearing to Avrohom.
During this meeting Avrohom notices that three travelers are passing by, and he runs to invite them into his home.
Avrohom is the model of hospitality. He runs to prepare food for them. (Incidentally, when he was getting calves to prepare for the meal, one calf ran away and Avrohom chased it as far as the cave of Machpella, where Adam and Chava are buried. Avrohom noticed the scent of Gan Eden there, so that's why later in the Torah he buys this property to bury his wife Sarah upon her death.)
These three travelers are really three angels, and one of them says that Sarah, Avrohom's wife, will have a son in one year.
The angels ask Avrohom where his wife Sarah is, and Rashi says one reason they asked was to pass her the Kos Shel Brocha -- the cup of blessing on the wine they held while saying the Grace after the meal. The Talmud learns from this, that passing the wine to one's wife gives tremendous blessings to her, as we see from the miraculous birth of Yitzchak soon after. The book Hayom Yom, in the entry for the date of the Lubavitcher Rebbe's wedding anniversary, encourages us to bench with wine.
In the second aliyah the angels depart to destroy the cities of Sodom and Amora. Avrohom attempts to bargain with G-d by asking that the cities be forgiven if they contain only 50 righteous people, then less and less until G-d agrees to forgive the cities for the sake of even ten righteous people.
In the third aliyah the angels arrive in Sodom and Avrohom's nephew Lot is waiting at the gate of the city looking for guests, as he learned from his uncle Avrohom.
Lot brings the guests into his house to stay. Unfortunately word of his guests spread, and the people of the city surrounded Lot's house. They demand the guests so they can harm them. Lot refuses. The angels take Lot and his wife and daughters outside the city and tell them to escape to the mountain before the city is destroyed.
The fourth aliyah continues with Lot's escape from Sodom. As Lot is escaping, his wife looks back and becomes a pillar of salt.
Eventually, Lot and his two daughters take shelter in a cave. The two daughters think the whole world is destroyed as with the flood at the time of Noach, so they decide that they need to re-populate the world through their father.
At the end of this aliyah Avrohom's wife Sarah conceives, and gives birth to a son. Avrohom performs a bris mila on him when he is 8 days old, and names him Yitzchak.
The fifth aliyah tells us that Avrohom was a hundred years old when Yitzchak was born, and Rashi explains that the whole world rejoiced with Sarah because many barren woman the world over were remembered with her, and many sick people were healed.
Sarah nursed many women's children to show that she had actually given birth to Yitzchak (even though she was 90 years old).
Later, Sarah notices the bad ways of Yishmael and wants him to leave so as not to influence Yitzchak. G-d says to Avrohom: "Listen to your wife" (this verse is widely quoted to show that wives are held in such high esteem in the Jewish family).
The sixth aliyah tells us how the king Avimelech notices that G-d is with Avrohom in everything he does and therefore Avimelech is afraid of Avrohom. So Avimelech wants to make a treaty with Avrohom for three generations. Avrohom agrees to do it.
The seventh aliyah contains the story of the akaida -- the binding of Yitzchak.
This is the supreme expression of "mesiras nefesh" -- self sacrifice, and love of G-d, that we inherit from our father Avrohom. This is the tenth and final trial of Avrohom.
When Yitzchak is 37 years old, G-d tells Avrohom to offer his beloved son Yitzchak as a sacrifice on Mount Moriah. Avrohom wakes up early in the morning and proceeds to do as G-d tells him. When they reach their destination Avrohom builds an alter and binds (binds = "akaida") Yitzchak on it. Avrohom is about to sacrifice Yitzchak when an angel stops him. Avrohom notices a ram stuck in the bushes and sacrifices the ram instead of Yitzchak. G-d says to Avrohom that He will surely bless Avrohom and greatly increase his offspring like the stars of the heavens and like the sand on the seashore; and his offspring will inherit the gate of its enemy. G-d also tells Avrohom that all the nations of the earth shall bless themselves by his offspring, because he listened to G-d's voice.
This is the Torah reading on Rosh Hashanah. In addition, the shofar we blow on Rosh Hashanah is a ram's horn reminiscent of this story.
Later in this aliyah some genealogy information is given, and in it, we are told that Rivkah, Yitzchak's future wife, is born. They meet, and the wedding takes place, in next week's parsha, Chaya Sarah.