Rashi: It implies that one is only permitted to transcribe the written Torah, but not the oral Torah (wheres "Al-Pi ha'Devarim ha'Eileh" implies that only the oral Torah may be cited orally, ¹ but not the written Torah - Gitin, 60b). ²

Ramban #1 and Da'as Zekenim: It refers to the Seifer ha'Beris, ³ which presumably they accepted with 'Na'aseh ve'Nishma' and which Moshe then read out to the people. ⁴ Since Yisrael broke the covenant that Hashem made with them at Matan Torah, Hashem had to enter into a new covenant with them ⁵ which He would not break; and it was to that end that He now asked Moshe to write up the conditions of the new covenant.

Seforno: Despite the fact that, before the sin of the Eigel, Hashem had promised to give Moshe the Luchos that He had prepared and the Torah and Mitzvos that He had written (incorporating the entire written Torah), now that they had sinned, He would have to carve the second Luchos ⁶ and write the Torah and Mitzvos himself.

Rashbam: It is referring to the prohibitions of following other gods, entering into a covenant with the inhabitants of the land and of marrying their daughters and to the Mitzvah of Aliyah le'Regel, ⁷ upon which the covenant between Yisrael and Hashem depends, as the Pasuk goes on to explain.

Nedarim, 38a: Just as "P'sal l'cha" implies that the shavings of the Luchos belong to Moshe, so too "K'sav l'cha" implies that the Torah ¹ belongs to Moshe and his descendents exclusively - and it is due to his generous nature that he gave it over to Yisrael.

R. Bachye (citing Gitin 60b): The fact that the Torah writes ?al-Pi ha?Devarim ha?Eileh? and not ?al-Pihem? teaches us that what was handed to Moshe in writing may not be learned orally and what was handed to him orally may not be transcribed ¹ ? and the covenant that Hashem made with us will only be effective if we abide by that rule.

Rashbam: It is referring to the prohibitions of following other gods, entering into a covenant with the inhabitants of the land and of marrying their daughters and to the Mitzvah of Aliyah le'Regel, ² upon which the covenant between Yisrael and Hashem depends, as the Pasuk goes on to explain.

Gitin 60b #1: It teaches us that Hakadosh-Baruch-Hu made a covenant with Yisrael over the oral Torah ³ exclusively. ⁴

Gitin 60b #2: It implies that only the oral Torah may be cited orally, but not the written Torah.

Gitin, 60b #3: It implies that the majority of the Torah was given orally ⁵ and it is only the minority that is written.

Nedarim, 32a: It teaches the greatness of B'ris Milah, by virtue of the fact that the Torah places it on a par with the rest of the Torah. ⁶

Yerushalmi Pe'ah, 2:4: It teaches us that the oral Torah is more precious to Hashem than the written one. ⁷

R. Bachye #1 (citing the Tanchuma) and Moshav Zekenim: Because the Mishnah falls under the category of ?Hashem?s secrets? ¹ and if it would be written, the nations of the world would steal it ? just as they stole many parts of the written Torah and claim it was theirs ? and in what way would Yisrael be superior to them ² - to the nations who refused to accept the Torah in the first place? ³

R. Bachye #2: With reference to answer #1 ? so that the nations, having refused to accept the Torah, should not now be to keep it (including the Mishnah) and claim reward. ^{4 5}

Ramban: Because it was on account of Moshe that He made the covenant with Yisrael.

Hadar Zekenim: Bcause when Hashem told Moshe to write the second Luchos, the angels protested that the Torah should not to be given to man, ¹ until Moshe reminded them that Yisrael do not eat meat and milk, but they did - when they visited Avraham Avinu. At which Hashem declared that this is a winning answer, and that, based on it, He will make a B'ris with Yisrael.