(Beraisa - Tana d'Vei R. Yishmael): Hash-m taught to Moshe the Kelalos (essence of the Mitzvos) on Sinai. He taught to him the Peratim (details, during the 40 years in the Midbar) in the Ohel Mo'ed.

R. Akiva says, the Kelalim and Peratim were given on Sinai. They were repeated in the Ohel Mo'ed, and again in Arvos Mo'av (Sefer Devarim, in the 40th year in the Midbar).

(Beraisa (115b)): (Even) nowadays, Nochrim may offer Korbanos on a Bamah.

116b (Beraisa): "Daber El Bnei Yisrael" - Shechutei Chutz is forbidden only to Yisrael. Nochrim may build Bamos and offer on them.

(R. Yakov bar Acha): One may not help them (offer outside the Mikdash) or to be a Shali'ach for them.

(Rava): One may teach them how to offer;

The mother of Shevor Malka (the Persian king) sent a Korban for Rava to offer to Hash-m. Rava told Rav Safra and Rav Acha bar Huna to get two Nochri youths of the same age to offer it l'Shem Shamayim.

Chagigah 13a (R. Ami): We do not teach Divrei Torah to Nochrim - "Lo Osah Chen l'Chol Goy u'Mishpatim Bal Yeda'um".

Bava Kama 38a (Rav Yosef): "...Ro'ah va'Yater Goyim" - Hash-m saw that they were not keeping their seven Mitzvos, and released them from their Mitzvos.

Objection: Do they gain from their sins?!

Answer (Mar brei d'Ravina): No - it means, even if they fulfil their Mitzvos, they are not rewarded for them.

Question (Beraisa - R. Meir): "Asher Ya'aseh Osam ha'Adam v'Chai Bahem" teaches that even a Nochri who engages in Torah gets reward, just like a Kohen Gadol.

Answer: They are not rewarded like one who is commanded, rather like one who is not commanded.

(Beraisa): Romi sent two officers to learn the Torah; Chachamim taught them. They acknowledged the truth of every point, except for one.

The officers: How can it be that a Yisrael's ox that gores a Nochri's ox is exempt, but a Nochri's ox (even a Tam) that gores a Yisrael's ox pays full damage?

If one is liable only for "Shor Re'ehu (of his fellowman)", a Nochri should be exempt when his ox gored a Yisrael's ox;

If we do not expound "Shor Re'ehu" like this, a Yisrael should be liable when his ox gored a Nochri's ox!

Nedarim 38a (R. Yosi bar Chanina): Torah was only given to Moshe and his descendants. It says "write for yourself" and "carve for yourself." Just like the carvings belong to Moshe, also the writing. Moshe was generous and gave the writing to Yisrael - "a generous person will be blessed."

He meant that Pilpul (a sharp understanding of Torah) was given only to Moshe. (He generously shared this with Yisrael.)

Sanhedrin 59a (R. Yochanan): A Nochri who learns Torah is Chayav Misah. "Torah...Morashah Kehilas Yakov", it is an inheritance for Yisrael, but not for Nochrim.

Rambam (Hilchos Melachim 8:10): Moshe bequeathed the Torah and Mitzvos only to Yisrael - "Morashah Kehilas Yakov". It is also for anyone of another Umah who wants to convert.

Rambam (10:9): A Nochri who learns Torah is Chayav Misah. He may learn only his seven Mitzvos. If he learned Torah, we hit and punish him and tell him that he is Chayav Misah, but we do not kill him

Rambam (Hilchos Ma'aseh ha'Korbanos 19:16): One may not help Nochrim offer outside the Mikdash, for this is forbidden to Yisrael. One may teach them how to offer to Hash-m.

Shiltei ha'Giborim (Avodah Zarah 6a:1): In Sanhedrin we say that a Nochri who learns Torah is Chayav Misah for stealing Yisrael's inheritance. A Yisrael who teaches him transgresses "v'Lifnei Iver Lo Siten Michshol." This refers only to Toras Moshe and the Mitzvos, but one may teach to them Nevi'im and Kesuvim, which have consolation for Yisrael and rebuttals of Apikorsim. Perhaps this will cause him to change his way.

Rashba (Bava Kama 38a DH Lamadnu): The Nochrim who came to learn Torah learned well three times. Alternatively, they learned written Torah, Mishnah and Talmud. The Yerushalmi says so

Question: Why do we need a source to forbid teaching Torah to Nochrim? A Nochri is forbidden to learn, so one who teaches him transgresses "V'Lifnei Iver Lo Siten Michshol"! We cannot say that this applies to their seven Mitzvos, for it is a Mitzvah to teach them their Mitzvos!

Answer #1 (Tosfos Chagigah 13a DH Ein): If there is someone else they could learn from, e.g. another Nochri, Lifnei Iver does not apply.

Answer #2 (Maharsha Chidushei Agados Chagigah 13a DH Ein): One may teach to a Nochri his seven Mitzvos. He is Chayav Misah for learning other Mitzvos. Our Gemara forbids teaching the reasons and secrets of Mitzvos, even for their seven Mitzvos. Even their Mitzvos "Bal Yeda'um", i.e. they do not know the reasons and secrets behind them.

Answer #3 (Herchav Davar, on Amuk Davar Vayikra 18:5): A Nochri is forbidden only to learn how the laws are expounded. The Aseh forbids teaching even Halachos themselves. Shiltei ha'Giborim permits teaching to them Nevi'im and Kesuvim. Perhaps this is because the Isur to teacgh Drashos is from "Torah Tzivah Lanu Moshe", and this applies only to the Chumash, which has laws.

Answer #4 (Yad Eliyahu 48, citing Ein Yakov brought another answer, that after Matan Torah, when they did not want even their seven Mitzvos, they are not rewarded even for them, so one may not teach even this to them. Only before Matan Torah, a Nochri who engaged in his Mitzvos was like a Kohen Gadol.

Rebuttal (Yad Eliyahu): If so, we should have given this answer in Avodah Zarah! (Also, it is difficult to say that the verse teaches only about what was before Matan Torah - PF.) Zevachim 117 proved that even nowadays we may teach them. We may not offer Korbanos for Nochrim, but we may teach them how to offer. The Rambam rules like this. All the more so we may teach them their seven Mitzvos! Be'er Sheva permits to learn with Nochrim, but advises not to. This is unlike the Gemara! Rather, it is a severe Isur to teach them secrets of Torah, or Mitzvos that do not apply to them

Question: Why did Chachamim teach Torah to Nochrim (three times)? This is forbidden!

Answer #1 (Tosfos Bava Kama 38a DH Kar'u): The ruling authority forced them to teach them. We need not be Moser Nefesh to avoid teaching Nochrim. Alternatively, the Nochrim expressed desire to convert, like it says in Sifri (v'Zos ha'Berachah 344, which describes the episode slightly differently).

Yam Shel Shlomo (Bava Kama 4:9): We learn from the episode and Tosfos that one may not teach Torah to Nochrim for the sake of Shalom with the Malchus, and surely not for the sake of pay. We see that people who do so cause heresy. The Torah commanded not to write Torah she'Ba'al Peh to avoid this problem.

Answer #2 (Ro'oh, in Shitah Mekubetzes Bava Kama 38a): The Nochrim who came to learn pretended that they were Yisre'elim. If not, it would be forbidden to teach them. The Yerushalmi says so.

Gra (YD 246:22): If a woman learns Torah, she gets reward. She is no worse than a Nochri!

Shiyurei Berachah (on 246:6): It is a great sin even to teach a Nochri Aleph-Beis. Some say that R. Ami said that we are not Moser Divrei Torah to Nochrim to teach that we may not sell to them Sifrei Kodesh. This is not a Diyuk, but the law is true.

Shlah (Shevu'os Ner Mitzvah 102): It is a severe Isur to teach even one word of Torah to a Nochri. The Nochri is Chayav Misah for learning it; "v'Lifnei Iver Lo Siten Michshol" applies. One may teach them their seven Mitzvos. The Zohar is very stringent about this, and does not distinguish. Tola'as Yakov says that this is because one without a Bris has no share in Hash-m or remembrance in his Torah. He is called Tamei, and not Kadosh. This is why one may not teach even Aleph-Beis to a Nochri. He falsifies Hash-m's great name, for the entire Torah is names of Hash-m, and one may enter the Bris of the tongue, i.e. the Torah, only with the Bris of flesh. Korban Pesach hints to a matter of Kedushah, and it is forbidden to an Arel. All the more so the names of Hash-m are forbidden to an Arel!

Note: This does not explain why one may not teach a Nochris, or why one may teach a Yisrael who was not circumcised, e.g. due to danger.

Meshiv Davar (2:77): To write a Sefer Torah for Kara'im (who deny oral Torah) does not transgress teaching Torah to Nochrim. One may teach them written Torah. Hash-m commanded Yehoshua to write the Torah in 70 languages for the Nochrim! "U'Mishpatim Bal Yeda'um" refers to laws expounded from Torah. Tosfos understood like this. He based his question on the fact that they taught the Nochrim three times. This is because the Kelalim and Peratim were given on Sinai, repeated in the Ohel Mo'ed, and a third time in Arvos Mo'av. The written Torah was given on Sinai. Mishnah was given in the Ohel Mo'ed. Talmud, i.e. how the Mishnayos were derived from the Torah, was given in Arvos Mo'av. Pilpul was given only to Moshe. He generously shared this with Yisrael, i.e. in Arvos Mo'av. This is why he said "'v'Atah Shma Yisrael El ha'Chukim veha'Mishpatim Asher Anochi Melamed Eschem." These are the Drashos and how to derive them from Torah. One may not teach them to Nochrim - "u'Mishpatim Bal Yeda'um." One may not sell to Kara'im a Sefer Torah intended for Yisre'elim, but one may write a Sefer Torah for Kara'im.

Yad Eliyahu (48): Chagigah 13a explicitly forbids teaching Torah to Nochrim. This is even if there will be animosity or a little danger or for pay. One may not falsify the law due to animosity or fear. This is clear from Bava Kama 38a and Tosfos. One may not sell Kodesh Seforim to a Nochri who wants to learn. Why did the Rambam and Tur omit this? I say that it was obvious!