Why will the nations then sing the praises of Yisrael?
Rashi: Because as they well know, in spite of all the long and endless persecutions, Yisrael have remained faithful and clung to Hakadosh-Baruch-Hu throughout never forsaking Him.
Rashbam: The nations should praise (not Yisrael, but) Hashem due to His people - and believe in Him, 1 because His kindness to His people exceeds His kindness to all other nations. 2
Seforno: The Pasuk means that both the nations and Yisrael should praise Hashem 3 - the nations should acknowledge that He is Just - and that there is no injustice in Him, and Yisrael should give thanks and the voice of song. 4
Targum Onkelos, Targum Yonasan, Da'as Zekenim, Hadar Zekenim (in Pasuk 41), Rosh: Because Yisrael are fortunate in that Hashem punishes those who afflict them.
Rashbam: Because if they will believe in Him and worship Him, He will extend His kindness to them too.
Rashbam: As the Pasuk writes in Tehilim, 117:1.
Seforno: When "He takes revenge from them" - as the Pasuk writes in Tehilim, 67:5.
Seforno: When "He atones for them."
Which two acts of revenge is the Pasuk referring to?
Rashi: "Dam Avadav Yikom" refers to vengeance for the nations' murder of Yisrael, and "ve'Nakam Yashiv le'Tzarav", for taking their property by force. 1
Rashi: As the Navi states in Yo'el 4:19 and Ovadyah, 1:10.
What is the meaning of "Vechiper Admaso Amo"?
Rashi: It means that Hashem will appease His land and His people' 1 over all the Tzaros that they suffered at the hand of the enemy.
Seforno: It means that Hashem will atone for the land 2 and for the people, 3 for the Chilul Hashem that they caused with their evil deeds, and He is now returning His Shechinah in their midst. 4
Rashbam, Hadar Zekenim and Riva: It means that He will cleanse the blood of His people from the land, by spilling the blood of the enemy. 5
Rosh and Da'as Zekenim: It means that Yisrael will atone, by taking revenge from Edom.
Targum Onkelos and Targum Yonasan: It means that Hashem will atone on His land.
Kesuvos 111a: We learn via a Gezeirah Shavah "ve'Chiper Admaso Amo" and "Mizbach Adamah" - Yisro, Sh'mos, 20:21, that if someone is buried in Eretz Yisrael, it is as if he is buried underneath the Mizbe'ach.
Yerushalmi Kil'ayim, 9:5: When Meisim would arrive from Chutz la'Aretz to Eretz Yisrael, they would place some earth from Eretz Yisrael on the coffin before burying them, in order to atone for them - because the Torah writes "Vechiper Admaso Amo". 6
Oznayim la'Torah (citing the Tanchuma and Midrash Rabah in Eikev): It refers to the fruit of Eretz Yisrael, which atone for Yisrael in the form of Bikurim, T'rumos, Ma'asros and Menachos.
Rashi: When His people are comforted, the land is comforted too. See Tehilim, 85:2. See also Sifsei Chachamim.
When it lay desolate from all that was done in it.
Oznayim la'Torah: As if the Torah had written "Admaso ve'Amo".
Seforno: As the Navi writes in Yeshayah, 52:8.
Rashbam: As the Torah writes in Mas'ei Bamidbar, 35:33
QUESTIONS ON RASHI
Rashi writes that "ve'Nakam Yashiv le'Tzarav" refers to revenge for taking their property as it writes in Yo'el 4:19. But that Pasuk concludes "Asher Shafchu Dam Naki"?
Riva (citing R. Tam of Orleans): The Gemara in Bava Kama 119a states that, if one steals a P'rutah, it is as if he has taken the soul of his victim. Consequently, the Pasuk in Yo'el is referring to the robbery of the B'nei Yehudah's property as murder.
