Must a not married woman [Besula, Beula, divorcee, or widow] cover her hair?
It is forbidden for a married woman, or single girl, to walk in public with uncovered hair. The definition of the term single is as follows:
Divorcee/widow: The term single written above refers to a widow or divorcee, and they must cover their hair even when single. [Some Poskim rule that this obligation is merely Rabbinical. Accordingly, some Poskim are lenient in certain situations to be explained, to allow a widow or divorcee to uncover her hair in public. This refers to a situation in which if she covers her hair, she will lose her job, or if she is in a situation that covering her hair will ruin her prospects of finding a new husband. Most Poskim however reject this ruling and rule that there is no room for leniency even in the above pressing situations, just as is the law regarding any Biblical or Rabbinical obligation, and so is the standard practice amongst G-d fearing Jews. Even according to the lenient approach, she must cover her hair at all times of the day, week and year that the above necessities and worries are inapplicable, and there is thus no all-time allowance according to any opinion for a once married women to freely walk around with uncovered hair. Practically, the above situations of necessity are rarely applicable, as one can find a job or new husband regardless of if the hair is covered, and hence the allowance of the lenient opinion is irrelevant. In the rare case however that it relevant, those who would like to follow the lenient approach are to contact their Rav for a final arbitration on this matter.]
Besula-never yet married: A woman who was never yet married and is still a Besula/virgin, is not required to cover her hair.
Beula-Never yet married: Some Poskim rule a Beula who was never married must cover her hair, even if this is due to rape. Other Poskim rule it is not required, and so is the widespread custom.
 Michaber E.H. 21:2; Rambam Issurei Biya 21:17
 Beis Shmuel 21:5; Chelkas Mechokeik 21/2; Bach 21; Beir Heiytiv 21:5; Degul Merivava 21; Based on Yerushalmi Kesubos Halacha 1who states that once a woman was married, she does not uncover her hair even if she became divorced or widowed prior to having marital relations
 The reason: The reason even a widow or divorcee must cover her hair is due to Daas Yehudis, the laws of Tzenius that the Jewish people accepted upon themselves. [see next] Perhaps one can also suggest based on Kaballa, that just as a married woman must cover her hair in order to quash the Gevuros and Tzimtzumim which can potentially nurture the Kelipos [see Likkutei Torah Emor 32a], so too regarding a once married woman.
 Igros Moshe E.H. 1:57; Yabia Omer E.H. 4:3 based on M”A 75:3 and Shvus Yaakov 103 [Vetzaruch Iyun on his proofs from the M”A and Shvus Yaakov which are all dealing with a Besula and not an Almana or Gerusha!]
 The reason: While all agree that a married woman is Biblically required to cover her hair, due to Daas Moshe, a divorcee or widow is only required to cover her hair due to Daas Yehudis, which is a Rabbinical obligation of Tzenius. [Igros Moshe ibid]
 Igros Moshe E.H. 1:57; 4:32
 The reason: As there is a doubt as to whether the Mitzvah of covering the hair for a married woman is a positive Biblical command or a negative command [i.e. prohibition]. [Igros Moshe ibid based on his understanding of Rashi and Ritva] The practical ramification of whether it is a positive or negative command is regarding if one may be lenient in a situation that guarding the command will cause one a loss of 20% of their income. If the matter is a command and not a prohibition, then one may be lenient in such a case. [See Rama 656:1] Accordingly, by a married woman there is no room to be lenient, as Safek Deoraisa Lechumra, and we must suspect for the approach that it is a prohibition. However, by a Rabbinical command we may be lenient, as Safek Derabanon Lekula. [Igros Moshe ibid]
 Igros Moshe E.H. 1:57
 Igros Moshe E.H. 4:32
The reason: As this is considered a great need, and is no less of a consideration of losing 20% of one’s income, in which case one may be lenient.
 Yabia Omer E.H. 4:3; Dibros Eliyahu 9:157; Michzei Eliyahu 120; Lev Avraham Weinfeld 107
 The reason: As a) In truth covering the hair is a prohibition and is not a positive command. And b) The allowance of giving up a positive command if it costs one more than 20% of his income is only relevant to a command that does not have an action, and that is not connect with a prohibition. [See Yabia Omer ibid]
 Admur 75/4; Michaber 75/2; Beis Shmuel 21:5; Chelkas Mechokeik 21/2; Bach 21; Beir Heiytiv 21:5; Degul Merivava 21; M”A 75/3; P”M 75 A”A 3
 Chelkas Mechokeik 21/2; Implication of Beis Shmuel ibid; Beir Heiytiv ibid; Degul Merivava 21
 Panim Meiros 1:25; Pischeiy Teshuvah 21/2;