What does "Eglah Meshuleshes" mean?
Rashi #1, Onkelus and Ramban #1: It means three calves.
Rashi #2 (Eruvin 63a): "Meshuleshes" means (not three, but) the third-born, 1 or when the animal has grown up to a third of its full size
What did the three calves, goats and rams represent?
Rashi: The three calves hint to Par Yom Kipur, Par He'elem Davar Shel Tzibur and Eglah Arufah. The goats allude to the he-goat brought inside [the Heichal] on Yom Kipur, of Musfei Rosh Chodesh and of the Yamim-Tovim. The rams hint to Asham Vadai, Asham Taluy and the lambs of a Chatas Yachid.
Ramban: The Pasuk hints at the three types of Korbanos that Avraham's children would ultimately bring [from these species]
What do the Tor (turtledove) and Gozal (young bird) represent?
Rashi and Ramban: The Tor and Gozal represent the turtledoves and young doves that would be brought as bird-offerings. 1
Ramban asks: Hashem did not specify the second species of bird! ("Gozal" is a generic term for "young bird.")
Ramban: Either Avraham understood himself which species Hashem meant; or he chose a dove, and Hashem fixed it on Avraham's initiative. Hashem sometime follows the lead of Tzadikim, as Chazal say, "When a Tzadik decrees, Hashem carries it out" (See Shabbos 59b).
Opinions in the Midrash differ as to whether Avraham was also shown the Asiris ha'Eifah of the Korban Minchah. What is this dispute based on?
Maharal (Gevuros Hashem Ch. 8, p. 46): Rabbi Shimon says that Avraham was shown the glory of Yisrael, whereas the Minchah is a poor man's Kaparah, and in deficient form. The Rabanan hold that Avraham was shown the complete picture of the different types of Kaparah.
What is the meaning of these specific types and numbers of Korbanos?
Maharal (Gevuros Hashem Ch. 8, p. 46): Hashem showed Avraham 10 types of Korbanos (counting the birds as one type). Just as every type of sickness has its own specific remedy, so too with sin, which is a malady of the Nefesh. The number 10 represents totality.
The Midrash says that these four types of animals allude to the four kingdoms that would subjugate Am Yisrael. Why allude to this here, and what was the significance of splitting the animals in half?
Maharal (Gevuros Hashem Ch. 8, p. 48): All the kingdoms in the world which would subjugate the Jewish people are included under these four; they attempt to ruin the covenant between Hashem, and Avraham and his descendants. Those nations are represented by the animals; for they are like animals in contrast to Avraham. Hashem commanded Avraham to split the animals and pass between their halves, to cancel out their power. The bird was not split; it represents Edom. 1 Splitting is only meaningful regarding something large and important. Edom might appear important, as they dominated the world, but in truth they have no value of their own, only what they have stolen from others.
Rashi to 15:10, however, writes that the birds represent Yisrael.
QUESTIONS ON RASHI
Rashi writes: "'A three-fold calf (Eglah Meshuleshes)' - [i.e.] three calves." Why does Rashi explain in this way?
Mizrachi: Rashi follows the Midrashic interpretation of the Pasuk. If the intent was merely to use an animal to make a covenant, one type of animal would have sufficed. Rashi therefore explains the purpose of the various types of animals Avraham used. Rashi also needs to explain the answer to Avraham's question, "By what merit etc." (15:8); Hashem answered with this allusion to the Korbanos.
Gur Aryeh: Surely, "three calves" is the literal meaning of the verse as well. Just as many animals can collectively be called "Behemah" (6:7); many calves can be called "Eglah," and "three-fold" is an adjective that describes their number.
Rashi writes: "This hints to three bulls [that are used in Korbanos]
Gur Aryeh #1: Although in these cases, the type of animal used differs from those Korbanos that Rashi lists, the sin for which they are offered is the same, therefore they need not be counted. 2: Gur Aryeh #2: Rashi lists those Korbanos that atone for any member of the Jewish people or for the nation as a whole, whereas these Korbanos are to atone for specific individuals.
Rashi writes: "Three rams- the Korban Asham...." Why doesn't Rashi list the lamb offered as a Chatas by a Metzora (Vayikra 14:10)?