Genesis 21:1–34; Genesis 22:1–24
Day 1:
G‑d remembers Sarah, and gives her and Abraham a son, who is named Isaac (Yitzchak), meaning "will laugh"; Abraham is then one hundred years old, and Sarah ninety. Isaac is circumcised at the age of eight days.
Hagar and Ishmael are banished from Abraham's home and wander in the desert; G‑d hears the cry of the dying lad, and saves his life by showing his mother a well. The Philistine king Abimelech makes a treaty with Abraham at Be'er Sheba.
Day 2:
G‑d commands Abraham to sacrifice his son on Mount Moriah (the Temple Mount) in Jerusalem. Isaac is bound and placed on the altar, and Abraham raises the knife to slaughter his son. A voice from heaven calls to stop him, saying that it was a test; a ram, caught in the undergrowth by its horns, is offered in Isaac's place.
Day 1:
I Samuel 1:1–2:10
The haftorah for the first day of Rosh Hashanah describes the birth of the prophet Samuel to Elkanah and his wife Chanah, who had been childless for many years. This echoes the story discussed in the day's Torah reading, about Sarah giving birth to Isaac after many years of childlessness.
During one of her annual pilgrimages to Shiloh, the site of the Tabernacle, Chanah tearfully and quietly entreated G‑d to bless her with a son, promising to dedicate him to His service. Eli the high priest saw her whispering, and berated her, thinking that she was a drunkard. After hearing Chanah's explanation, that she had been whispering in prayer, Eli blessed her that G‑d should grant her request.
Chana conceived and gave birth to a son whom she called Shmuel (Samuel). Once the child was weaned, she brought him to Shiloh and entrusted him to the care of Eli.
The haftorah ends with Chanah's prayer, wherein she thanks G‑d for granting her wish, extols His greatness, exhorts the people not to be haughty or arrogant, and prophesies regarding the Messianic redemption.
Day 2:
Jeremiah 31:1–19
The haftorah for the second day of Rosh Hashanah talks about G‑d's everlasting love for His people, and the future ingathering of their exiles. In the last verse of this hauntingly beautiful haftorah, G‑d says, "Is Ephraim [i.e., the Children of Israel] not My beloved son? Is he not a precious child, that whenever I speak of him I recall him even more?" This follows one of the primary themes of the Rosh Hashanah prayers, our attempt to induce G‑d to remember us in a positive light on this Day of Judgment.
Jeremiah begins by affirming G‑d's love for the Jewish people. "With everlasting love I have loved you; therefore I have drawn lovingkindness over you."
Because of this love, G‑d assures His nation that they have a very bright future awaiting them. "I will yet build you up, then you shall be built forever, O virgin of Israel; you will yet adorn yourself with your tambourines, and go forth in joyous dance." Jeremiah then describes the ingathering of the exiles, when all of Israel will be returned to the Holy Land: "You will again plant vineyards on the hills of Samaria . . . Behold, I will bring [Israel] from the land of the north, and gather them from the ends of the earth . . . a large assembly will return here. Weeping with joy they will come, and with compassion I will lead them . . . I will turn their mourning into joy, and will console them and gladden them after their sorrow."
Jeremiah then describes the heavenly scene, where the silence is broken by the sound of bitter weeping. Our Matriarch Rachel refuses to be consoled, for her children have been exiled. G‑d responds: "Still your voice from weeping and your eyes from tears . . . There is hope for your future; the children shall return to their border."
For G‑d has heard the voice of the lad where he is (21:17)
The ministering angels hastened to indict him, exclaiming: "Sovereign of the Universe! Would You bring up a well for one who will one day slay Your children with thirst?" "What is he now?" asked G‑d. "Righteous," said the angels. Said G‑d: "I judge man only as he is at the moment."
(Midrash Rabbah; Rashi)
https://w2.chabad.org/media/pdf/133842.pdf