In the previous parsha, Vayeira, we read about the birth of Yitzchak Avinu in his parents old age, and the story of the binding of Yitzchak, - the akaida.
In the first aliyah we find out that Sarah Imanu, Yitzchak's mother, has passed away. Rashi comments on the words used by the Torah to describe her age: that at one hundred, she was without sin as a twenty year-old, and at twenty, she was as beautiful as a girl of seven.
This aliyah then gives a detailed account of Avrohom purchasing the cave of Machpella for 400 shekels of silver. It is interesting to note, that the Cave of Machpella (Chevron), the site of Bais Hamikdash bought by King David, and the city of Shchem, bought by Yakov and later used to bury Yosef-- were all paid for, but yet all are contested today.
After the story of the akaida at the end of the last parsha, Avrohom realized that Yitzchak, who was 37 years old, should be getting married. At the very end of that parsha, in the maftir reading, some genealogy information was given including the birth of Rivkah, which was to be Yitzchak's future wife. So in this second aliyah, the Torah begins the story of Avrohom sending his servant Eliezer back to the land of Avrohom's birth to find a wife for Yitzchak.
In the third aliyah Eliezer arrives at Avrohom's homeland and waits outside the city by the well of water. Here he prays to G-d that his mission of finding a wife for Yitzchak should be quickly successful. He prays that he will ask a young lady for a drink of water, and when she answers, she will say "of course, and I'll also give your camels water to drink." But before he finishes speaking, a young lady approaches and he asks for a drink, and she says "of course" and offers also to feed his camels. And naturally, she turns out to be from the correct family, too.
In the fourth aliyah, after Eliezer found Rivkah so quickly, he says "Boruch Hashem!" Rivkah runs to tell her family about this man by the well, and her brother, Lavan, goes out and greets Eliezer and invites him to spend the night. Eliezer accepts and goes and meets Avrohom's future in-laws and tells them all that has transpired, and they agree to the match.
In the fifth aliyah Eliezer and Rivkah's family celebrate, and in the morning Eliezer asks that he be allowed to return immediately to his master with Rivkah. But her family wants to hold her for a year. In the end they ask Rivkah, which, Rashi says, teaches us that a woman can't get married against her will.
Eliezer and Rivkah return and find Yitzchak praying in a field as it was getting to be evening. Actually, our sages say that this was the invention of the Mincha (afternoon) prayer.
The wedding takes place and Yitzchak takes Rivkah to his mother Sarah's tent. When Sarah lived, this tent had three constant blessings: the candles burned from Shabbos to Shabbos, the dough was blessed, and the cloud of the Shechina rested over the tent. When Rivkah entered the tent, these three blessing returned. Incidentally, these three blessings correspond to the three special mitzvot of Jewish woman: Lighting Shabbos candles, the taking of challah which is associated with a kosher home, and Taharas Hamishpocha -- the observance of the laws of family purity -- a G-d given gift to the Jewish people for the spiritual and physical health of the family.
In the sixth aliyah Avrohom remarries, but Rashi says his wife was the original Hagar that he was married to before. And in this aliyah, Avrohom Avinu passes away at the age of 175, and Yitzchak and Yishmael bury their father in the cave of Machpella where Sarah, his wife, and Adam and Chava, are also buried.
Because, as we saw in the previous aliyah, that Yishmael had done teshuva and participated in Avrohom Avinu's burial, the Midrash says that he was rewarded by having his genealogy described in this, the seventh aliyah.