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Hatarat Nedarim and Shevuot is the annulment of vows and oaths, which can sometimes be used to annul a vow by a group of three people. For general laws of Nedarim see Hilchot Nedarim.
Nedarim and Shevuot Subject to Hatarah
- The Geonim introduced strict safeguards against their generations' imprudence in taking Nedarim by declaring Nedarim and Shevuot impossible to annul, but many Rishonim dismissed their sheltering attitude as a stumbling block for those who did take Nedarim and Shevuot. If one doesn't annul his Nedarim, he'll cease to seek annulment and just violate his Nedarim intentionally. Therefore, it's better to annul the Nedarim than let them be violated, even if it was taken with Hashem's name. Some recommend not getting involved unless it's for a Mitvah purpose, community peace, or the like, and not to annul Nedarim that have a trace of sin either. Others also advise the Chacham to impose a monetary or fasting penalty on the one seeking Hatarah to discourage his taking further Nedarim.
- If one performed a good practice 3 times and didn't say he was doing it Bli Neder and now he wants to nullify the practice, he should perform Hatarat Nedarim. 
How Many Dayanim
- Hatarat Nedarim should be done in front of three people who know how Hatarat Nedarim functions.
- Even though according to the letter of the law an expert individual (Yachid Mumcheh) can annul Nedarim on his own, we do not have anyone who fits this status nowadays according to the Shulchan Aruch.
- A Beit Din of two people cannot perform Hatarat Nedarim.
- It's recommended to perform Hatarat Nedarim in front of ten people so that one is able to annul a Nidduy Chalom.
- According to Rav Tzvi Pesach Frank, seemingly only the majority of the Dayanim need to agree to annul the vow, like by monetary cases, and not all of them.
Who May Sit on the Beit Din
- One may not perform Hatarat Nedarim in the location of his Rebbe or someone greater than him without permission.
- Women and children may not serve as Dayanim for Hatarat Nedarim; however, one may gather three Dayanim in addition to the thirteen year old whose maturity status has not yet been determined and tell only the lad the details of the Neder.
- One who prohibits himself from benefiting from certain people may not use them on the Beit Din to annul his Neder, but it would work post-facto. Others reverse the case, that only if he prohibits himself from giving benefit to certain people may they not serve as Dayanim. In such a case, some say a Chacham from that city can include people who are from elsewhere on the Beit Din, while others disagree.
- Similarly, one who swears to not become a Gabbay or trustee of the city may not seek annulment from the Chacham of the city.
- If one prohibits himself to the entire Jewish people, it's like a Bediavad case, so he may ask anyone to annul his Neder for him.
- One Beit Din can annul numerous Nedarim of numerous people with one Hatarat Nedarim ceremony.
- Hatarat Nedarim should be done in a language that one understands, otherwise it isn't valid.
- The judges should sit for Hatarat Nedarim and the petitioner should stand.
- The judges repeat "Muttar Lach," "Mufar Lach," or "Machul Lach" three times.
Charatah and Petach
- The simplest means of annulling a Neder is through the sincere regret (Charatah) of the one who took the Neder (the Noder). If such Charatah exists, then the Beit Din may proceed and annul the Neder, but, if it does not, they must search for a different way out, a Petach. For example, one who takes a Neder not to benefit from someone who wronged him, can have it annulled with just Charatah if he discovers that the individual did not actually wrong him and therefore regrets the Neder. At the same time, if he does not regret the Neder but rather now seeks Hanaah from the individual for some other reason, he can not immediately have his Neder annulled. It must rather be scrutinized by a Beit Din until they find an alternative door out, a Petach.
- Insincere, phony regret put on just to convince the Beit Din to annul the Neder leaves the Hatarah ineffective.
Whose Nedarim Can Be Annulled
- Minors need not perform Hatarat Nedarim.
- The common practice is that woman do not perform hatarat nedarim and rely on the Kol Nidrei said prior to Yom Kippur. A woman may appoint her husband to do Hatarat Nedarim on her behalf and it is effective, yet one shouldn't convene a bet din specially for this purpose.
- Hatarat Nedarim may be done at night and with relatives. Some say that although Hatarat Nedarim may be performed if one of the judges is a relative of the petitioner, it may not be performed if two of the judges of the Bet Din are related to one another.
- For all the details of Hatarat Nedarim on Shabbat, see Nedarim on Shabbat. In general, one should not do Hatarat Nedarim on Shabbat if the Hatarat Nedarim isn't needed for Shabbat. For a congregation there is room to be lenient regarding performing Hatarat Nedarim on Shabbat or on Yom Kippur itself.
- The custom is to do hatarat nedarim on erev rosh hashana and erev yom kippur. 
Here is the text of Hatarat Nedarim on daat.ac.il
- Shulchan Aruch Yoreh Deah 230:1
- Beit Yosef and Rama Yoreh Deah 230:1, Ben Ish Chai (Shanah Shniah, Re'eh 24). See Birkei Yosef Yoreh Deah 230:1 and 234:1
- Shach Yoreh Deah 230:1
- See Shulchan Aruch YD 214:1, Minchat Shlomo 1:91:20
- Shulchan Aruch YD 228:1 writes that one may do Hatarat Nedarim in front of 3 hedyotot. The Shach YD 228:2 explains that they don't need to be knowledgeable in halacha as long as they know how Hatarat Nedarim works. Ben Ish Chai (Shanah Shniah, Re'eh 24)
- Shulchan Aruch Yoreh Deah 228:1
- Ben Ish Chai (Shanah Shniah, Re'eh 24)
- Chazon Ovadyah (p. 263)
- Shu"t Har Tzvi Yoreh Deah 189. He cites Yevamot 25b as a proof, but Chacham Ben Tzion Abba Shaul (Kitvei HaTalmidim ad loc, printed in Yeshurun vol. 38 page 221, rejects his proof.
- Shulchan Aruch Yoreh Deah 228:2
- Though we allow one to annul his Nedarim at night, with relatives, and standing, all of those disqualifications are external to one's own status as a viable Dayan. Rabbi Akiva Eiger Yoreh Deah 228:1, Shu"t Rabbi Akiva Eiger Hashmatot Siman 73
- As Pirut HaNeder is only MiDeRabbanan, so one can rely on the Chazakah. Pitchei Teshuva Yoreh Deah 228:2
- Shulchan Aruch Yoreh Deah 228:5
- Shach Yoreh Deah 228:10
- Taz Yoreh Deah 228:8, Shach Yoreh Deah 228:12
- Shulchan Aruch Yoreh Deah 228:6. See Taz Yoreh Deah 228:9 who finds difficulty with this ruling and its ramifications.
- Shach Yoreh Deah 228:11
- Rama Yoreh Deah 228:2
- Chayei Adam 138:8, Kitzur Shulchan Aruch 128:16. See Rama Yoreh Deah 228:3
- Shulchan Aruch YD 228:2-3 writes that the judges may perform Hatart Nedarim while standing if they uproot the Neder using Charata (regret) but should sit if they are uprooting the Neder using a Petach (a opening). Shach Yoreh Deah 228:9 writes that since the minhag is always to uproot a Neder using a Petach, the minhag is that the judges sit for the Hatarat Nedarim.
Taz Yoreh Deah 228:7 writes that the petitioner need not stand, but the Shach also writes the minhag is that he does stand. Rabbi Akiva Eiger (comments on Shulchan Aruch YD 228:1) quotes the Maharikash who argues that the petitioner must stand, however, after the fact he fulfilled his obligation if he said it sitting.
- Though, according to the Rambam, once is sufficient, the Shulchan Aruch Yoreh Deah 228:3 recommends three times to concretize the matter. Shach Yoreh Deah 228:6
- Shulchan Aruch Yoreh Deah 228:4
- Shulchan Aruch Yoreh Deah 228:4
- Shearim Metzuyanim BeHalacha 128:24
- Rav Schachter in a shiur entitled "Inyonei Rosh Hashana" (min 40-3) on yutorah.org. see also Rabbi Eli Mansour who writes that although women are required to make Hatarat Nedarim, customarily a husband represents his wife when he stands before the Bet Din for Hatarat Nedarim. In fact, the text that we use explicitly mentions that one seeks absolution of his own vows as well as the vows of his wife. Furthermore, women customarily attend the Kol Nidreh service on Yom Kippur, which is also effective in annulling one’s vows.
- Shulchan Aruch YD 228:3 writes that Hatarat Nedarim may be done at night and with relatives.
- Rabbi Hershel Schachter in a shiur on Inyonei Yom Kippur (min 40-2) quotes Rav Aharon Soloveitchik as having ruled that while a relative could perform Hatarat Nedarim in front of a Bet Din with his relative as one of the judges, one may not perform Hatarat Nedarim in front of a Bet Din which has two judges who are related to one another. A support for this ruling is Rabbi Akiva Eiger (comments on Shulchan Aruch YD 228:1) who writes that while relatives can serve as a Bet Din for Hatarat Nedarim, a woman can't serve on such a Bet Din.
- However Rav Shmuel Wosner (M'bet Levi 5754, p. 15, n. 3) held that the judges could be relatives to one another.
- Chazon Ovadyah (Yamim Noraim p. 263)
- Kaf Hachayim 581:12, Yalkut Yosef Moadim page 22, Yabia Omer OC 2:30, Chazon Ovadia Yamim Noraim page 42, Aruch Hashulchan OC 581:12