Gemara

A voice from Heaven: That chest is for the wife of R. Chanina ben Dosa. She will put in it Techeiles for Tzadikim in the world to come.

Menachos 42a (Rav Yehudah): A Nochri cannot make Tzitzis, for it says "Daber El Benei Yisrael v'Asu Lahem Tzitzis." Yisraelim can make Tzitzis, but Nochrim cannot.

Gitin 45b (Rav Hamnuna - Beraisa): A Sefer Torah, Tefilin, or Mezuzah written by an informer, Nochri, slave, woman, minor, Kusi, or Yisrael Mumar is Pasul.

"You will bind... and you will write" - only one who is commanded to wear Tefilin is qualified to write them.

Avodah Zarah 39a: A certain woman married a Chaver (pious man), and would tie Tefilin on his arm. She later married a tax collector (he is assumed to steal), and helped tie the seals (receipts for those who paid) on his arm.

Rishonim

Rambam (Hilchos Tzitzis 1:12): If a Nochri made Tzitzis, it is Pasul, for it says "Daber El Bnei Yisrael v'Asu Lahem Tzitzis." If a Yisrael made Tzitzis without intent, it is Kosher. If Tzitzis were made from what was already made, it is Pasul.

Hagahos Maimoniyos (9): The Ri and Rabbeinu Yehudah derived from here that women are Kosher to make Tzitzis, for we exclude only Nochrim. Rabbeinu Yehudah permitted his wife to make Tzitzis. My Rebbi says that they should not make Tzitzis, for it says "Bnei Yisrael... v'Asu", but they may make the garment and spin the threads. A case occurred in which a woman inserted the Tzitzis into the garment, and R. Tam disqualified it. We find that a woman tied Tefilin on a Chaver's arm. We must say that she only helped him to tie it. Alternatively, a woman is disqualified only to make the matter herself, e.g. write, make Tzitzis or tie a Lulav, but she may tie (Tefilin), for this is not making the Mitzvah. I say that the same applies to spinning thread for Tzitzis. Bava Basra 74b proves this.

Rosh (Gitin 4:46): R. Tam learns from the Beraisa here that a woman cannot make Tzitzis or tie a Lulav. If she did, it is Pasul, for she is not commanded. In Menachos we disqualify a Nochri who made Tzitzis, for we require "Bnei Yisrael." This implies that a woman is Kosher. We say in Sukah that a woman's Sukah is Kosher. In Bava Basra, it says that R. Chanina ben Dosa's wife will put Techeiles for Tzadikim in the world to come. A woman is Pasul only for a Sefer Torah, which we learn from Tefilin and mzu through a Gezerah Shavah. We do not learn to other Mitzvos.

Korban Nesanel (40): The Taz (OC 14:1) says that even R. Tam permits women to spin thread for Tzitzis. This is wrong, for if so there is no proof from Bava Basra. (Perhaps R. Chanina ben Dosa's wife will spin thread for Techeiles!)

Einayim l'Mishpat (Bava Basra 74b): The Taz holds like Hagahos Maimoniyos, who is stringent about making Tzitzis and lenient about spinning thread for Tzitzis. He explains (according to R. Tam) that our Gemara teaches that she will spin thread for Tzitzis. The Rashbam and R. Gershom explain that she will store Techeiles for Tzadikim. If so, there is no proof at all.

Mordechai (Hilchos Ketanos (after Menachos) 949): Some disqualify women, just like we expound regarding Tefilin that only one who is commanded to wear is Kosher to write. The Ri disagrees. Bnei Yisrael excludes only a Nochri. Women would be commanded to wear Tzitzis if the Mitzvah applied at all times! They are disqualified only from Tefilin. Our custom is that women make Tzitzis. Maharam did not allow this, for one who is exempt cannot exempt one who is obligated. I say that this is only l'Chatchilah. If not, why is a woman's Sukah Kosher?

Poskim

Shulchan Aruch (OC 14:1): If a Nochri made Tzitzis it is Pasul.

Mishnah Berurah (1): We are concerned only for putting the Tzitzis in the garment and making the first knot and windings. A Nochri may do the rest of the knots and windings, which are only l'Chatchilah. The Rosh says that a Nochri may spin or twine Tzitzis.

Question (Nezirus Shimshon 14, brought in R. Akiva Eiger 1): We require spinning Lishmah (for the sake of the Mitzvah), and the Rosh is Machshir when a Yisrael supervisies. All the more so we should be Machshir making Tzitzis (in such a case), for the Rambam does not require Lishmah for this!

Answer (R. Akiva Eiger): We disqualify making Tzitzis due to a Gezeras ha'Kasuv "Bnei Yisrael... v'Asu", not due to Lishmah. Therefore, even Yisrael supervision does not help. This is how the Rosh explains the need for the verse, even though he requires making them Lishmah, for he holds that a Nochri with Yisrael supervision is considered Lishmah. The Rambam holds that it is not Lishmah; this forced him to hold that Asiyah need not be Lishmah (for if not, we would not need "Bnei Yisrael... v'Asu").

Kaf ha'Chayim (1): If a Yisrael and a Pasul slaughtered together, the Beis Yosef disqualifies and the Shach is Machshir (YD 2:11). They argue similarly about a Yisrael and Nochri who made Tzitzis together. We follow the Beis Yosef.

Shulchan Aruch (ibid): A woman may make Tzitzis.

Beis Yosef (DH uv'Hagahos): The custom is to be lenient, for the majority permit, and they have a proper reason.

Question (Magen Avraham 2): We always exclude women from "Bnei Yisrael" (Kidushin 36a, Menachos 61b)!

Mizrachi (Reish Parshas Emor): In the entire Torah it says "Bnei Yisrael", yet women are equated to men for all laws, i.e. they are commanded about all Mitzvos. We exclude women only when "Bnei Yisrael" is superfluous, or regarding a Mitzvas Aseh sheha'Zman Gerama (it does not apply at all times).

Chachmas Shlomo: I say that there is no argument. A woman cannot make Tzitzis by herself for a man to wear, but she can be a man's Shali'ach to make Tzitzis. Even though one cannot be a Shali'ach for a matter that does not apply to him, women may fulfill a Mitzvas Aseh sheha'Zman Gerama. All the more so it applies to her according to the opinions that she may bless on such Mitzvos! According to the opinion that a slave cannot receive his own Get of freedom, it applies to him (and he can make a Shali'ach to receive his Get) because he can receive a Get for another slave of a different master (Kidushin 23b). A woman can fulfill Tzitzis herself, and make Tzitzis for herself, therefore, she can be a Shali'ach for a man. The Mechaber allows a woman to be a man's Shali'ach. The Rema disqualifies when she is not a Shali'ach; we learn this from "Bnei Yisrael."

Rema: Some are stringent to require men to make them. It is good to do so l'Chatchilah. If a Yisrael made Tzitzis without intent, it is Kosher. If Tzitzis were made from what was already made, it is Pasul.

Magen Avraham (3): This opinion is stringent about every Mitzvah that women are exempt from, e.g. Sukah and Lulav. A minor is like a woman.

Magen Avraham (649:8): The Rema holds that if a Nochri tied a Lulav, it is Kosher b'Di'eved. We hold that a Lulav need not be tied. If so, it is not part of the Mitzvah, so we should permit a Nochri l'Chatchilah! We must say that since it beautifies the Mitzvah, it is like the Mitzvah itself.

Mishnah Berurah (2): Even if a man stands by her, it is Pasul due to "Bnei Yisrael... v'Asu."

Mishnah Berurah (3): Women may spin and twine the Tzitzis.

Mishnah Berurah (4): It is proper that a minor less than 13 not make Tzitzis. One may use a boy above 13 years even if he did not bring two hairs. Eretz ha'Chayim allows using a minor l'Chatchilah if an adult supervises and tells him to make them Lishmah. If he made them without adult supervision, one must untie them and make them again.

Kaf ha'Chayim (4): One may use a boy above 13 only if he brought two hairs.

Mishnah Berurah (5): If a woman put the Tzitzis in, b'Di'eved it is Kosher even without a man supervising. She is believed to say that she did so Lishmah.