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1) [line 1] PARAH (PARAH ADUMAH/HAZA'AH)
(a) The Parah Adumah, an exclusively red-haired female cow is burned on Har ha'Zeisim and its ashes are used for making a person Tahor if he is Tamei Mes. Only a cow that has not had a yoke placed upon it and has had no other work done with it is fit to be used as a Parah Adumah. A place is prepared for its slaughter on Har ha'Zeisim, opposite the gate to the Azarah (the courtyard of the Beis ha'Mikdash). After it is slaughtered, its blood is sprinkled in the direction of the Beis ha'Mikdash seven times. This is the "Haza'ah" to which the Gemara now suggests the Mishnah is referring. A cedar branch, some Ezov branches and a piece of crimson wool are thrown into the carcass of the cow while it is burning. (Bamidbar 19:1-22)
(b) If a person (or utensil) became Tamei through touching Tum'as Mes or being in the same room as a Mes or something that is Metamei b'Ohel, he must wait seven days to become Tahor. On the third and seventh days he must have spring water mixed with the ashes of the Parah Adumah (Mei Chatas) sprinkled on him. A person who is Tahor dips three Ezov branches that have been bound together into the mixture, and sprinkles them on the person who is Tamei. On the seventh day, he immerses in a Mikvah after the mixture is sprinkled on him in order to complete his Taharah. (Bamidbar 19:17-19)

2) [line 1] HO'IL V'HAYESAH LAH SHE'AS HA'KOSHER - since it had a moment at which it was fit to be used as food (i.e. right after it was slaughtered)

3) [line 1] PARAH NIFDEIS AL GABEI MA'ARACHASAH - the Parah [that is intended to be used as the Parah Adumah] may be redeemed even after it was slaughtered and placed on the wood to be burned

4) [line 11] TEREIFAH - an animal with a mortal blemish
5) [line 16] KIL'AYIM (KIL'EI BEHEMAH) - an animal that is a crossbreed [between a sheep and a goat]

6) [line 29] ZEH BANAH AV (BINYAN AV)
In the Introduction to the Sifra (the Halachic Midrash to Vayikra), Rebbi Yishmael lists thirteen methods that Chazal use for extracting the Halachah from the verses of the Torah. One of them is called Binyan Av. A Binyan Av (lit. "building through a father" -- father in this sense means a Biblical source), is a rule of Biblical interpretation in which one subject is deemed a prototype in order to apply a Halachah stated in that subject to other comparable subjects.

7) [line 32] "SHOR O CHESEV O EZ..." - "When an ox or sheep or goat [is born, it shall remain with its mother for seven days, and from the eighth day and onward it will be acceptable as a Korban, a fire-offering to HaSh-m.]" (Vayikra 22:27)

8) [line 32] NIDMEH - An animal that does not appear to be of the same species as its mother or father, e.g. the parents are goats and it has the appearance of a sheep.

9) [line 34] SHE'IY ATAH YACHOL L'HOTZI KILAYIM MI'BEINEIHEM - for it is impossible to bring forth a crossbreed from them (i.e. from an ox and a sheep, because the species are too different from each other, for a Behemah Gasah (such as an ox) gives birth after nine months, while a Behemah Dakah (such as a sheep) gives birth after five months)

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