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1) [line 1] "CHEREV" HAREI ZEH K'CHALAL - a sword is like a corpse
(a) Any metal utensil that touches a dead body is given the same level of Tum'ah as the dead body itself, i.e. it becomes an "Avi Avos ha'Tum'ah." Similarly, if a metal utensil touches an Av ha'Tum'ah, it becomes an Av ha'Tum'ah. (A Rishon or Sheni l'Tumah cannot make utensils Temei'im.)
(b) According to some Rishonim, this law applies to non-metal utensils (except for earthenware) as well -- see Insights to Pesachim 14b.

2) [line 1] AV HA'TUM'AH HU (THE DIFFERENT LEVELS OF TUM'AH: TUM'AS OCHLIN)
(a) All objects belong to one of three categories: 1. Sources of Tum'ah 2. Objects that can become Tamei 3. Objects that cannot become Tamei
(b) All sources of Tum'ah are called Av ha'Tum'ah, except for a corpse, which can generate more Tum'ah than any other object and is therefore referred to as the "Avi Avos ha'Tum'ah."
(c) When one object makes another object Tamei, the second object has a weaker Tum'ah than the first. If something becomes Tamei from an Av, it is called a Rishon l'Tum'ah, or Velad ha'Tum'ah. A Rishon makes a Sheni l'Tum'ah. (Liquids are an exception to this rule. The Chachamim decreed that liquids should always be a Rishon, even if touched by a Sheni.)
(d) A Sheni l'Tum'ah cannot make Chulin Tamei mid'Oraisa. Even mid'Rabanan, there is no such thing as Shelishi L'Tum'ah with regard to Chulin. Terumah, however, can become a Shelishi L'Tum'ah. (Also, if someone guarded his Chulin from Tum'ah as one normally guards Terumah, it is called "Chulin she'Na'asu Al Taharas Terumah," and can become a Shelishi.)
(e) Terumah that is a Shelishi l'Tum'ah cannot make other Terumah Tamei. However, it may not be eaten. It is referred to as "Pasul" (invalid) rather than "Tamei." Kodesh (objects associated with the sacrifices) that is touched by a Shelishi l'Tum'ah can become a Revi'i. A Revi'i of Kodesh is also called "Pasul." (For a full discussion of the principles of Tum'os and Taharos, see Insights to Pesachim 14:1-2.)

3) [line 3] ITMI B'SHERETZ - he became Tamei with Tum'as Sheretz (TUM'AS SHERETZ)
(a) A Sheretz (a crawling pest -- see Vayikra 11:29-38 and Background to Menachos 29:25), even if it or a part of it is only the size of an Adashah (lentil bean), is an Av ha'Tum'ah (Chagigah 11a). It makes a person or object Tamei at the level of a Rishon l'Tum'ah through Maga (contact), whether the Sheretz was touched willingly or unwillingly. The person who becomes Tamei by touching a Sheretz may not eat Terumah or Kodshim or enter the Azarah of the Beis Ha'Mikdash. However, he can immediately immerse in a Mikvah. After nightfall he becomes Tahor and may eat Terumah or Kodshim or enter the Azarah.
(b) In addition to Tum'as Maga, a dead Sheretz that is found in an earthenware oven makes the oven and all food or drink items that are in it Temei'im, whether the Sheretz touches them or not.
(c) In our Sugya, the person who touches a Sheretz becomes a Rishon l'Tum'ah. He can make the food and drinks that he touches Temei'im, but he cannot Metamei utensils, and, as such, he cannot cause the Shechitah knife Tamei.

4) [line 4] SHE'BADAK (BEDIKAS SAKIN)
In order to perform Shechitah (ritual slaughter) properly, the slaughtering knife has to be checked to make sure it is not nicked in the slightest way.

5) [line 4] KEROMIS SHEL KANEH - the hard outer sheath of a reed (PESHUTEI KELEI ETZ: TUM'AH )
(a) The Torah states that wooden utensils can become Tamei if they are touched by a person or object that is an Av ha'Tum'ah, of if they are under the same Ohel as a dead person (Vayikra 11:32, Bamidbar 31:20). However, since the Torah compares a wooden object that becomes Tamei to a sack ("Sak"), the wooden object must have certain qualities in common with a sack in order to become Tamei.
(b) Among these qualities are: 1. The object must have a receptacle, i.e. an area in which it can contain other objects, as opposed to a flat board (with the exception of a "Tavla ha'Mis'hapeches" -- see Background to Menachos 96:34:c). Objects that do not have receptacles are called "Peshutei Klei Etz." 2. It must not be large enough to hold 40 Se'ah, for if it is that large it cannot be transported when filled, as opposed to a sack, which is made to be transported either empty or full. 3. It must be an object that is sometimes transported, and not one that is always stationary. If it is left stationary, it is called a "Kli he'Asuy l'Nachas" and is not Mekabel Tum'ah.

6) [line 5] TZOR / TZUR - a sharpened stone
7) [line 6] ZECHUCHIS - a piece of glass

8) [line 7] KUSI (KUSIM)
(a) The King of Ashur brought the people of Kusa to Eretz Yisrael and made them settle in the Shomron. They converted to Judaism after they found themselves under attack from lions. The Chachamim disagree as to whether their conversion was honest and valid (Geirei Emes) or not (Geirei Arayos - converts because of lions).
(b) After the times of the Mishnah, the Kusim were found worshipping an image of a dove and the Chachamim gave them the status of Nochrim. (According to most Rishonim, this means that they decided to treat them like Nochrim l'Chumra, even if they were Geirei Emes. According to the RAMBAM (Peirush ha'Mishnayos), however, this means that they decided that their conversion was not sincere and deemed them Nochrim (Geirei Arayos) for all Halachic matters.)
(c) The Kusim kept many Mitzvos of the Torah down to their last detail. For example, Matzos that were baked by the Kusim, besides being perfectly free of Chometz, were fit to be used for the Mitzvah d'Oraisa of eating a k'Zayis of Matzah Shemurah on the Seder night (Tosefta Pesachim 2:2, Kidushin 76a). As is evident from our Sugya, they were also meticulous with regard to Shechitah. However, there were other Mitzvos that they did not keep at all. For example, the Kusim did not refrain from causing others to sin (which is prohibited by the verse, "Lifnei Iver Lo Siten Michshol" - "You shall not put a stumbling block before the blind" -- Vayikra 19:14). They interpreted this verse literally, stating that it only applies to a stumbling block, and only before the blind.
(d) One of the Halachos about which the Kusim were not careful was the requirement of Kidushin (betrothal) before marriage. Kidushin forms a bond of husband and wife that is only severed by a Get (bill of divorce), but Kusim would not give a Get after effecting Kidushin with a woman. It is possible that one Kusi effected Kidushin with a woman and another Kusi married her before she received a Get from her first husband, a situation that led Chazal to fear that many of their offspring might be Mamzerim (RASHI to Yevamos 37a).

9) [line 18] HA'MENI'ACH OVED KOCHAVIM B'CHANUSO (YAYIN NESECH / STAM YEINAM)
(a) Wine that was poured as an idolatrous libation is Asur b'Hana'ah. This is derived from the verse, "Asher Chelev Zevacheimo Yochelu, Yishtu *Yein Nesicham*" - "Those who ate the fat of their sacrifices, and drank the wine of their drink offerings" (Devarim 32:38), which compares the wine of libations to an animal sacrificed for idolatrous purposes.
(b) The Chachamim prohibited the wine of a Nochri that was *not* poured as a libation ("Stam Yeinam") out of fear that drinking wine together would lead to intermarriage. In order to avoid confusion between Yayin Nesech and Stam Yeinam, the Chachamim instituted that Stam Yeinam is also Asur b'Hana'ah (one of the "Eighteen Decrees" -- Shabbos17b). Although this is only an Isur mid'Rabanan, it is a very severe prohibition (see Chochmas Adam 75:1).

10) [line 21] HA'SHOMER - one who watches [wine to make sure that it is not touched by the Nochrim]

11) [line 33] YISRAEL MUMAR (MUMAR L'SEI'AVON / MUM'AR L'HACH'IS)
There are two types of Mumarim (apostates). The first type is one who transgresses l'Sei'avon, one who rejects the Mitzvah or Mitzvos due to his desires. The second type of Mumar is one who rejects the Mitzvos out of arrogance, in order to anger HaSh-m (l'Hach'is).

12) [line 34] LE'ECHOL NEVEILOS L'SEI'AVON - to eat Neveilos (meat from an animal that was killed without a proper Halachic slaughtering) because of his desires. RASHI explains that this person prefers to eat meat that is Kosher. However, if Kosher meat is not available, or if the slaughtering knife that he has is not fit for slaughtering, he will eat non-Kosher meat or slaughter the animal anyway (causing it to become Neveilah).

13) [line 13] SAKIN PEGUMAH - a knife with nicks or dents
14) [line 14] MUMCHIN - people who know the Halachos of Shechitah
15) [line 15] MUCHZAKIN - people who have slaughtered successfully two or three animals in front of others

16) [line 27] MUCHZAKIN AF AL PI SHE'EIN MUMCHIN - people who have slaughtered successfully two or three animals in front of others, but the others do not know that the people who slaughtered know the Halachos of Shechitah

17) [line 29] NIS'ALEF - one who faints or becomes weak at the sight of blood (RASHI)

18) [line 50] KUSIM GEREI ARAYOS HEN - see above, entry #8

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