Gemara

(Rav): The wife of Ohn ben Peles reasoned (Gra) that they are all virtuous - "Ki Chol ha'Edah Kulam Kedoshim." She sat outside and uncovered her hair. Anyone who came to get Ohn turned away, so he was never called to come with Korach's asembly.

Berachos 24a (Rav Sheshes): A woman's hair is considered Ervah -- "Sa'arech k'Eder ha'Izim."

Gitin 90a: If a man does not protest when he sees his wife go out with uncovered hair... he is a Rasha. It is a Mitzvah to divorce such a woman.

Kesuvos 72a (Mishnah): A woman is divorced without a Kesuvah for Overes Al (transgressing) Das Yehudis, e.g. going out with her head uncovered...

Question (Tana d'Vei R. Yishmael): "He will uncover her hair" warns (married) Benos Yisrael not to go out with uncovered hair. (This is mid'Oraisa!)

Answer: Mid'Oraisa, Kalasah (a basket that can be worn on the head) suffices. This does not fulfill Das Yehudis.

(R. Asi): Kalasah suffices (even for Das Yehudis).

Question (R. Zeira): In the market this does not suffice. He cannot discuss in the Chatzer (courtyard), for no Bas Yisrael is careful about this!

Answer (Abaye): It suffices in the Mavoy (alleyway), between Chatzeros.

Shabbos 64b (Mishnah): A woman may go out with strands of hair, whether the strands are from her own (detached) hair, or from another woman.

Rishonim

The Rif and Rosh (Kesuvos 32b and 7:9) bring the Gemara in Kesuvos.

Ran (DH mid'Oraisa): The Torah uncovers a Sotah's hair to disgrace her Midah k'Neged Midah for uncovering her hair for the Bo'el. This shows that this is forbidden. Alternatively, since it says to uncover her hair, we infer that until now it was covered, for such is the way of Bnos Yisrael.

Rosh (Berachos 3:37): Hair of a married woman is Ervah, for they normally cover it. The hair of virgins is usually uncovered, so one may read Shema when facing it.

Kesef Mishneh (Hilchos Kri'as Shema 3:16): The Gemara said that a woman's voice and hair are Ervah. The Rambam holds that this does not refer to Kri'as Shema. Rather, one may not benefit from her voice or look at her hair. Therefore, he did not mention these here.

Rambam (Hilchos Isurei Bi'ah 21:17): Bnos Yisrael may not go in the market with their heads uncovered. This applies to single and married women.

Poskim

Shulchan Aruch (OC 75:2): One may not read Shema when facing hair of a woman that is normally covered.

Beis Yosef (DH Kosav, citing the Rashba): The Ra'avad says that the Rif omitted all this because the Gemara said that even buttocks are not Ervah, and all the more so an exposed Tefach, thigh, voice or hair. The Ra'avad disagrees. Here we discuss what distracts a man. We said that buttocks are not Ervah only regarding her herself (to bless when her buttocks are exposed), or her husband when they touch him (but he does not see them), for he is used to his wife. L'Halachah, we hold like the Rambam (that one may say Shema while facing them), but l'Chatchilah it is good to be stringent about hearing a woman sing or seeing her hair while saying Shema.

Kaf ha'Chayim (13): The Shulchan Aruch forbids. He retracted from wat he wrote in Beis Yosef (that it is merely good to be stringent), for the Rosh and Tur explicitly forbid, and the Rif and Rambam omitted this. He did not retract regarding voice, for the Rosh does not forbid this particularly regarding Kri'as Shema.

Mishnah Berurah (10): Even if they cover it only in the market but not in the Chatzer or house, all agree that it is Ervah even in the house. One may not read Shema if part of it was exposed. Further, even if this and other women go with exposed hair in the market, like lewd women, it is forbidden. This is like an exposed thigh, for the Torah forbids exposing her hair. 'That is normally covered' excludes virgins, who need not cover their hair, or hair that leaves the net. This is Ervah only in a place where people are particular that no hair leave the net.

Rema: This refers even to his own wife.

Kaf ha'Chayim (15): Keneses ha'Gedolah says that the Mechaber permits regarding one's own wife. What is his source?! The Mechaber forbids an exposed Tefach regarding his own wife, and the same applies to everything else. The Rema often explains what is not explicit in the Mechaber. Many Acharonim say that also the Mechaber forbids his own wife.

Shulchan Aruch (ibid): The hair of virgins is usually uncovered, so it is permitted.

Question (Magen Avraham 3): The Shulchan Aruch (EH 21:2, below) and Rambam forbid even Penuyos (single women) to go in the market with their heads uncovered! We find that an exposed head (at the time of Nisu'in) was a sign of a virgin (Kesuvos 15b)! If the Shulchan Aruch refers to single widows, he should have specified. Perhaps in EH the Shulchan Aruch discusses unbraiding the hair, and this is forbidden even for a Penuyah. Rashi (Bamidbar 5:18) explains "he will expose her hair" in this way. We cannot say that the Torah forbids this, for if so it is forbidden even if her head is merely exposed, for we learn from Sotah that Bnos Yisrael may not go with their heads uncovered. Rather, we must say that it is merely modesty for a Penuyah.

Mishnah Berurah (12): Machatzis ha'Shekel and Magen Giborim permit Penuyos to unbraid the hair. The Chayei Adam was unsure whether Nochriyos, who go with exposed hair, are like Penuyos.

Kaf ha'Chayim (16,17): Since it depends on Hirhur, if their hair is normally covered, one may not read facing it. European women always go uncovered, so one may read facing it, but one may not intend to look, even at hair outside the net.

Rema: The same applies to hair of (married) women that normally leaves the net, and all the more so Pe'ah Nochris (a wig), even if she usually covers it.

Beis Yosef (DH Tefach): The Rashba explains that we are not concerned for hair that normally leaves the net. Since he is used to it, it does not distract him.

Mishnah Berurah (13): One may read Shema facing such hair, but one may not intend to look at it.

Magen Avraham (4): Maharam Alashkar says that if a woman came from a place where women do not expose (hair that leaves the net) to a place where they expose, if she does not intend to return, it is forbidden in the market, but permitted in the Chatzer. The Zohar is very stringent that no hair of a woman be seen, and it is proper to do so.

Mishnah Berurah (14 and Kaf ha'Chayim 18): The Zohar says that if any of her hair is seen even in the house, it endangers her house and makes the Satan enter her house. If she is careful to cover it, her husband and children will be blessed.

Magen Avraham (5): The correct text of the Shulchan Aruch permits a wig. Be'er Sheva says differently. His words are difficult.

Eshel Avraham: Be'er Sheva permits only if the wig is covered. We are not concerned lest she (rely on the wig and) remove the cover. Where women go with uncovered wigs, they may rely on the Shulchan Aruch, which permits. Perhaps a proof is from Kesuvos 72a, which asks that the Torah forbids an uncovered head. We did not say that she has a wig, and transgresses Das Yehudis if it is uncovered. This shows that going with an uncovered wig does not transgress Das Yehudis.

Gra (7): Shabbos 64b permits (exposed detached hairs).

Mishnah Berurah (15): If the custom is that women do not go out with an exposed wig, one should be stringent, due to Mar'is Ayin.

Kaf ha'Chayim (19): The Acharonim permit, like the Rema.

Shulchan Aruch (EH 21:2): Bnos Yisrael may not go in the market with their heads uncovered. This applies to single and married women.

Bach, Chelkas Mechokek (2), Beis Shmuel (5), Taz (12), Be'er Heitev (5): This refers to single women who are not virgins.

Gra (11): 'Bnos Yisrael' (Kesuvos 72a) includes virgins.

Pischei Teshuvah (2): The Magen Avraham (above) says that it includes virgins, i.e. to unbraid the hair. Dagul me'Revavah proved from the Yerushalmi that virgins are permitted.