Dora Bas Rivka Silver O'H
G-d told Avram that He took him from Ur Kasdim to give him Canaan as an inheritance. Avram worried that he or one of his descendants might do something to disqualify themselves, so G-d made a pact with Avram to "seal the deal." He had Avram take a variety of animals and birds. G-d then had Avram split the animals (but not the birds) in half and place the have opposite one another. (This was a symbolic act, signifying that the two portions were really one whole. Similarly, the two parties in the pact - in this case G-d and Avram - were of one mind, as it were.) Vultures came to eat the animal carcasses, but Avram drove them off.
The sun was going down and G-d caused Avram to fall into a deep sleep, wherein he had a vision. In it, G-d told Avram that his descendants would be in a foreign land for 400 years, during which time they would be oppressed and enslaved. G-d said that He would judge the oppressing nation and redeem Avram's descendants with great wealth. Avram himself would be buried in peace and his descendants would return four generations later. It became quite dark and G-d caused a smoking furnace and a flaming torch to pass between the animal parts. G-d told Avram that He granted him the land of the various Canaanite nations.
Sarai had not had any children, so she told Avram to have a child using her servant, an Egyptian woman named Hagar, as a surrogate. Avram did as his wife had bade. Hagar conceived, which made her look down on Sarai, who had been unsuccessful in that area. Sarai complained to Avram that Hagar had become insubordinate and Avram replied that Sarai should handle the situation as she saw fit. Sarai clamped down on Hagar, who fled rather than toe the line.
Hagar stopped to rest by a desert oasis. An angel appeared to her and asked where she was going. When Hagar explained that she was running away from Sarai, the angel encouraged her to return and to fall into line. Hagar was destined to give birth to a great nation. She was instructed to name her son Yishmael (Ishmael - :G-d will hear"), signifying that G-d had heard her prayer. Yishmael would be rebellious by nature, involved in controversy, but he would live over his brothers. Hagar praised G-d for this and called Him a seeing G-d (or a G-d of visions). The spring where the angel appeared to her came to be known as the Well of the Living One of Vision (Beer LaChai Ro'i - it's less cumbersome in Hebrew). Hagar returned to Sarai and later gave birth. Avram named the child Yishmael. Avram was 86 at this time.
Flash forward 13 years. Avram is now 99 and Yishmael is 13. G-d appeared to Avram and He informed him that he was about to perform a mitzva that would perfect him. This mitzva would be the sign of the covenant between G-d and Avram. Because of this covenant, G-d was changing Avram's name to Avraham (Abraham), adding the letter Hei of G-d's own Name to Avram's. This new name would signify Avraham's role as the father of many nations. Kings would be among his descendants. (The forging of this covenant continues in the next aliyah.)