Rashi: 'You will only be considered wise in the eyes of the nations (when you study the words of the Torah) if you will not forget them and fulfill them correctly, but if you will make them crooked due to forgetfulness, they will consider you fools.

Ramban: Following the warning to keep all the Mitzvos, the Chukim and the Mishpatim, the Torah is now issuing a warning (a Mitzvas Lo Sa'aseh) never to forget Ma'amad Har Sinai, the source of all the Mitzvos, with everything that they saw and what they heard there - the thunder, the flashes of lightning, Hashem's Kavod and His Greatness, and how they heard His words coming from the fire. And then to pass all of this on to their children and grandchildren. ¹

B'rachos, 32b: It is a warning against endangering one's life. ¹

Shevu'os, 36a: It is a warning against cursing oneself. ²

Ba'al ha'Turim: "The Neshamah of man is the lamp of Hashem" (Mishlei, 29:27). 'Guard My lamp', says Hashem, 'and I will guard your's.

Avos, 3:8: It is a warning that, anyone who forgets any of his learning, it is as if he is guilty of his own death - provided he is not an Oneis (he was not lax in revising what he learned ¹ - Torah Temimah). ²

Menachos, 89b: It teaches us that anyone who forgets any of his learming - see answer #1 - transgresses one, two or even three La'avin. ³

Ramban: Before presenting the Aseres ha'Dibros, the Torah wants to impress upon us the fact that it is Hashem who gave us the Torah. Had we received it from Moshe Rabeinu - notwithstanding the fact that his Nevu'ah was supported through signs and wonders, if a subsequent Navi or dreamer would arise and issue commands that clash with the Torah (that we heard from Moshe), and verify his words with a sign or a wonder, it would create a doubt in our minds as to the veracity of Moshe's words. But now that we received it from Hakadosh-Baruch-Hu Himself, without a medium - borne out by what we saw and heard at Har Sinai, ¹ we will have no doubt that whoever tries to make any change in the Torah is an imposter.

Seforno: It is a warning being influenced by the Apikorsim's heretical arguments ² in the process of proving them wrong - and subsequently forgetting both what we saw on Har Sinai and the explanations that we heard from Moshe.

Ibn Ezra: See Yisro Sh'mos, 20:15. ¹

Oznayim la'Torah: It refers to the Aseres ha'Dibros, which Yisrael miraculously saw - black letters on white fire.

Yerushalmi B'rachos, 5:1: It refers to learning in depth, ² and teaches us that someone who learns in depth will not easily forget what he has learnt.

Kidushin, 30a #1: It teaches us that a father is obligated to teach his grandson ¹ Torah. ²

Yerushalmi Kidushin, 1:7: It teaches us that one is obligated to marry off one's sons when they are young. ³ However if he did not do so, he himself is obligated to get married in order to fulfil "ve'Hoda'atam le'Vanecha". ⁴

Kidushin, 30a #2: If someone teaches his son ⁵ Torah, it is considered as if he taught himself, his son and his son's son, for all generations.

Kidushin, 30a #3: When someone teaches his grandson ⁶ Torah, it is considered as if he he received it from Sinai ⁷ (which the next Pasuk discusses).

Oznayim la'Torah: Once Torah has been taught to three conseutive generations, it will never be forgotten. ⁸

Refer to 4:9:1:2.

B'rachos, 21a: The juxtaposition of "Yom asher Amadta ... " to "ve'Hoda'atam le'Vanecha ... " teaches us that Ba'alei Keryin are forbidden to learn Torah - just as they were forbidden to receive the Torah at Har Sinai. ¹

B'rachos, 22a: The juxtaposition of "Yom asher Amadta ... " to "ve'Hoda'atam le'Vanecha ... " teaches us that learning Torah must be performed with dread and with fear, with trembling and with sweat, in the same way as the Torah was given. ² This prompted the Chachamim to forbid Ba'alei Keryin to learn Torah but to permit Metzora'im and Bo'alei Nidos to do so. ³