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1) [line 7] TA'AM K'IKAR - The flavor of the food is considered like the essence of the food
A food that is prohibited to eat that has given its flavor to another food or drink into which it was mixed, causes the entire mixture to become prohibited (i.e. it is not Batel b'Rov). (See Background to Pesachim 44:2)

2) [line 18] KIL'EI HA'KEREM
(a) It is forbidden to plant different types of crops together as it states in the Torah, "Sadecha Lo Sizra Kil'ayim," - "Do not plant different species (together) in your field." (Vayikra 19:19), and "Lo Sizra Karmecha Kil'ayim, Pen Tikdash ha'Melei'ah ha'Zera Asher Tizra u'Sevu'as ha'Karem." - "You shall not sow your vineyard with other species, lest the fruit of the seed which you have sown, and the fruit of the vineyard, be forfeited." (Devarim 22:9). If one sows Kil'ayim, the produce becomes prohibited ('Kidesh,' from the word in the verse, 'Tikdash').
(b) The Mishnayos in Maseches Kil'ayim specify the distance that one must leave in between different crops.

3) [line 20] ORLAH
(a) In the first three years after a fruit tree is planted, its fruits are called Orlah and are Asurim b'Hana'ah, as it states in Vayikra 19:23.
(b) If a person eats a k'Zayis of Orlah fruit, he receives Malkos. If he derives benefit from Orlah (or any other food that is Asur b'Hana'ah), according to most Rishonim he is punished with Malkos (TOSFOS Chulin 120a DH Ela), while according to others, he is only punished with Makas Mardus, a Rabbinic institution of Malkos. (RAMBAM Hilchos Ma'achalos Asuros 8:16 -- see also Mishneh l'Melech to Hilchos Yesodei ha'Torah 5:8)

4) [line 33] BASAR B'CHALAV
(a) The verse, "Lo Sevashel Gedi ba'Chalev Imo" - "You shall not cook a young lamb in its mother's milk," is written in the Torah three times; in Shemos 23:19, in Shemos 34:26, and in Devarim 14:21.
(b) These three verses prohibit 1. cooking meat and milk together, 2. eating them after they have been cooked together, and 3. deriving any benefit from them after they have been cooked together. By Torah Law it is forbidden to consume milk and meat that was *cooked* together; the Chachamim instituted that it is forbidden to consume meat and milk together in any fashion.
(c) One reason given for this law is that meat represents death (the slaughter of the animal), while milk represents new life, and it is not proper to mix life and death (REKANATI, TZEROR HAMOR, ZOHAR 2:124b). Another reason given is that eating meat and milk together was an idolatrous practice, especially on festivals (MOREH NEVUCHIM 3:48; RALBAG). Alternately, mixing meat and milk is prohibited because it is causing a detrimental change in nature, just like the prohibitions of Kil'ayim (SEFER HA'CHINUCH #92, #113)

5) [line 37] KIL'AYIM
See above, entry #2.

6) [line 39] D'IY SARU LEI KULEI YOMA B'CHELBA, SHARI - if meat is soaked in milk for an entire day, it is permitted to be eaten (mid'Oraisa. Mid'Rabanan it is prohibited,)

7) [line 1] GI'ULEI OVDEI KOCHAVIM - the prohibition to use utensils of non-Jews (without Kashering them) because the non-kosher food that they absorbed will be expelled into the food that is cooked in them (Bamidbar 31:21-24, Pesachim 44b)

8) [line 7] NOSEN TA'AM LI'FEGAM - An Isur that spoils the taste of the food into which it falls
(a) An Isur (prohibited food item) that is Nosen Ta'am li'Fegam, i.e. it does not forbid the food into which it falls (Avodah Zarah 67b). The Rishonim explain that the Halachah of Ta'am k'Ikar (see above, entry #1) does not apply to Isur that spoils the taste of a mixture since one who eats the mixture does not benefit in any way from the Isur that is mixed into it (RASHBA and RAN ibid.). An Isur that stands by itself remains prohibited even if its taste spoils, as long as it is still fit to be eaten by animals.
(b) Nosen Ta'am li'Fegam permits a mixture even if the Isur itself has a pleasant taste, but when mixed into another food, it spoils the taste of the mixture. It permits a mixture even if the Isur spoils the taste of the mixture only because of an external factor (e.g. not enough salt) (Avodah Zarah 65b, 67a, SHULCHAN ARUCH YD 103:1-4).
(c) Because an Isur that is Nosen Ta'am li'Fegam does not prohibit the food into which it is mixed, Rav Chiya (Avodah Zarah 75b) states that the Torah forbids cooking in a utensil that was used to cook non-Kosher food only if the utensil is Ben Yomo (i.e. it was used to cook non-Kosher food that same day). Otherwise, non-Kosher Ta'am the utensil absorbed spoils, and it detracts from, rather than enhances, the taste of the food that is subsequently cooked in the utensil. RASHI and TOSFOS write that a utensil is not Ben Yomo if it was left overnight. The RASHBAM and the SHULCHAN ARUCH (YD ibid. 103:5-7) rule that the utensil is not Ben Yomo only if it was left unused for twenty-four hours after cooking the non-Kosher food.

9) [line 10] KEDEIRAH BAS YOMA - a pot that was used to cook non-kosher food that same day

10) [line 11] IY EFSHAR D'LO PAGMAH PURSA - it is impossible that the taste of the Isur does not spoil the taste of the mixture, at least slightly

11) [line 19] CHATAS
(a) If a person transgresses a sin b'Shogeg (unintentionally) for which he is liable to Kares b'Mezid (intentionally), he is liable to bring a Korban Chatas. The Korban Chatas is a female goat or sheep. Since it is one of the Kodshei Kodashim (the highest sanctity of sacrifices), it may only be slaughtered in the northern part of the Azarah and may only be eaten in the Azarah by Kohanim. Before its slaughter, the owner presses his hands on the head of the animal (Semichah) and confesses his sin.
(c) Regarding a Korban Chatas, the Torah states "Kol Asher Yiga bi'Vesarah Yikdash..." - "Whatever shall touch its flesh shall be holy..." (Vayikra 6:20). This verse exhibits the Halachah of a piece of meat that gets a Beliyah (an infusion of Ta'am (lit. taste) brought about through any form of transference, e.g. cooking) from a Chatas. If the Chatas was Pasul, the meat also becomes Pasul; if the Chatas was Kosher, the meat must be eaten according to the stringent Halachos of a Chatas. Only Kohanim may eat it for one day and following night in the Azarah.

12) [line 20] SHNEI KESUVIN HA'BA'IN K'ECHAD EIN MELAMDIN
(a) 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 by that subject to other comparable subjects.
(b) If two verses express the same Halachah regarding two different subjects, we cannot apply the Halachah elsewhere through a Binyan Av. Through the fact that the Torah found it necessary to repeat the law the second time, we may deduce that the Halachah is *not* meant to be applied automatically in all situations.

13) [line 25] TE'ACHEL KA'CHAMUR SHE'BAH - [the meat that gets a Beliyah from a Chatas] must be eaten according to the more stringent Halachos of the two Korbanos. (Normally, the Chatas is the more stringent of the two, and as such, only Kohanim may eat the meat for one day and following night in the Azarah. If, however, the meat of a Korban Chatas gets a Beliyah from a Korban Shelamim on the day *after* its slaughter, even the meat of the Chatas may only be eaten until nightfall of *that* day, and not during the following night.)

14) [line 26] V'RABANAN, TZERICHEI - it seems that our Gemara learns that according to the Rabanan, the Halachah of Ta'am k'Ikar must be written in both Nazir and Chatas, because it is impossible to learn one from the other. However, the Gemara in Pesachim 45a learns that Heter Mitztaref l'Isur is the Halachah that cannot be learned from Chatas to Nazir (TOSFOS to Pesachim 45a DH v'Rabanan)

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