What does the Torah mean when it writes that they saw the G-d of Yisrael?
Rashbam: They saw 'similar to the Pasuk "and you will see My Back". 1
Ramban #1 (citing Ibn Ezra): They saw Hashem, but in a prophetic vision. 2
Targum Onkelos and Targum Yonasan: They beheld "the Glory of the G-d of Yisrael". 3
What Moshe was shown after the sin of the Golden Calf (Ki Sisa, Sh'mos 33:23. See Rashi there). The Pasuk cannot be taken literally (See Tosfos Kidushin 49a DH 'ha'Metargem').
Why does the Torah refer to Hashem as 'The G-d of Yisrael'?
Ramban #1: To teach us that the merit of Yisrael their father was with them when they experienced this vision.
Ramban (according to Kabalah): Because, at Har Sinai, the Torah wrote 1 "Vayedaber Elokim", 2 it writes here that they beheld "Elokei Yisrael", to teach us that the elders saw more than the rest of the people. 3
In Yisro, Sh'mos 19:25.
With reference to the Pasuk in Va'eschanan, Devarim 5:21 "Hein Her'anu Hashem Elokeinu es Kevodo ve'es Godlo ... " (Ramban).
What is the meaning of "under His Legs"?
Rashi (in Shabbos, 113b): With reference to "Elokei Yisrael", it means 'underneath Him".
Seforno: If "the G-d of Yisrael" was in the Heaven, then "under His legs" refers to the earth. 1
Targum Onkelos: It means 'underneath His Throne'.
Targum Yonasan: It means 'underneath His foot-stool'.
Moreh ha'Nevuhim (1:28): It means 'due to Him.'
What was the "Livnas ha'Sapir"? What did it symbolize?
Seforno: It was radiance, which has no color. It hints to the human soul, which is [initially] empty of all knowledge, and is prepared to receive it through investigation as it chooses.
Rashbam: Beneath the Feet of the G-d of Yisrael, they saw something that resembled the whiteness of a sapphire.
Moreh ha'Nevuchim (1:28): It was understanding that just like radiance has no color, Hashem first created a formless matter [and later formed the world from it].
Targum Yonason: It was a sapphire brick formed from a fetus that a young girl miscarried, and it fell into the mud that she was kneading. Hadar Zekenim - during the slavery, it was in front of Him. After the redemption, He placed it under His feet, and there was light and Simchah in front of Him. Then, when the Churban occurred, He threw it to the ground. 4
Rosh: It was a Shefir (the sac in which a fetus grows; the word Sapir alludes to this). A woman miscarried it, due to the labor in Egypt. When Hashem wanted to drown the Egyptians in the sea, the Sar of Egypt complained. Gavriel brought the Shefir up to Shamayim to recall the labor of making bricks.
Sotah, 17a: It was a brick colored Techeiles (dark blue or turquoise) which resembles the Kisei ha'Kavod. 5
Which Hashem now showed Yisrael to demonstrate that He was with them in their troubles.
Targum Yonasan: As the Pasuk states in Eichah, 2:1 "Hishlich mi'Shamayim Eretz Tiferes Yisrael ve'Lo Zachar Hadom Raglav".
Sotah (Ibid.): With reference to the Techeles of Tzitzis, the Gemara states that Techeiles resembles the sea, the sea resembles the sky and the sky, the Kisei ha'Kavod
Why does the Torah add the word "ke'Ma'aseh Livnas ha'Sapir"?
Yerushalmi Sukah, 4:3: To treach us that the Egyptians did not only make them manufacture bricks, but they made them do all sorts of labor connected with bricks.
Oznayim la'Torah: It was to demonstrate to Yisrael that the harsh slavery had achieved its effect, inasmuch as their souls had now become pure like a sapphire and brought them close to the Shechinah
What does the "clarity of the heaven for purity" mean?
Rashi: Refer to 24:10:6:1.
Rashbam and Targum Yonasan: It refers to the sky when it is clear of clouds.
Ramban: It refers to 'the sky that resembles the fearful ice that was spread above the heads of the Chayos (ha'Kodesh)' that Yechezkel saw. 1
Seforno: The Nefesh of the Galgal (the sphere on which heavenly bodies revolve) is devoid of any physicality.
Hadar Zekenim: There are different appearances of sapphire. They saw like the color of a clear sky, like Techeles. 2
What does "the clarity of the heaven for purity" symbolize?
Rashi: It symbolizes the light and joy that Hashem felt when Yisrael left Egypt. 1
Seforno: Just like the Nefesh of the Galgal is devoid of any physicality, so the human soul is totally non-physical.
In contrast to the sapphire brick which symbolized the slavery in Egypt and which Hashem had now removed from before Him.
Why did Hashem show Yisrael the sapphire brick only now and not at the Yam-Suf?