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- There's a dispute whether Havdalah is Deorittah or Derabbanan. 
Havdalah for Yom Tov
- After Yom Tov, which is followed by a regular weekday or a day of Chol HaMoed, one should say Havdalah. However, if a Yom Tov is followed by a Shabbat, there is no Havdalah. 
- Havdalah at the end of Yom Tov only consists of the Bracha of HaMavdil and there is no bracha of Besamim or Ner. 
Who is Obligated
There's a dispute whether women are obligated in Havdalah.
- Nonetheless, according to Sephardim women may make the it for themselves. 
- Some Ashkenazim hold that women should not recite Havadalah for themselves, while many others say that if a woman can not find someone to hear Havdalah from, she should recite Havdalah for herself.  Some say that a woman can even say the beracha on the fire.  Others disagree. 
- Once a child has reached the age of Chinuch (5 or 6) the parents should train him in hearing havdalah 
Havdalah in Davening
- See the Atta Chonantanu page.
- If Motzei Shabbat is a Yom Tov, in middle of Atta Bechartanu, one should insert VeTodiyanu in place of Atta Chonantanu. 
The order of Havdalah
- The order of the Brachot of Havdalah is Yayin (Hagefen), Besamim, Ner (Meorei HaEsh), Havdalah (Hamavdil). 
- The custom is to add several pesukim prior to Havdalah for a good sign. For the full Ashkenazic text see here. For the full Sephardic text see here. 
Havdalah recited by the cantor
- The cantor recites Havdalah in the synagogue on behalf of those who have no wine or who will not recite Havdalah for himself in his home. Whoever wishes to can listen to the cantor's Havdalah in the synagogue and fulfill his obligation, even thought the listener is not holding a cup of wine. It is a widespread minhag ion our times for the cantor to recite Havdalah in synagogue, and there is no need to protest the custom. It should be made clear to the congregation, however, that everyone must recite Havdalah at home on behalf of his family members who have not heard it in the synagogue, even though he himself did hear it. 
- The cantor must sit down when he recites Havdalah in the synagogue, and all those of he congregation who wish to fulfill their obligation by listening to him must sit while he recites it. 
- The opinion of the Geonim is that whoever recites Kiddush or Havdalah must drink at least melo lugmav of the wine, and if he does not he has not fulfilled his obligation of Kiddush or of Havdalah . This opinion should be followed in practice, and therefore the person who is chosen to recite Havdalah in the synagogue must be someone who will be able to drink melo lugmav. If the only person capable of reciting Havdalah is someone who cannot drink that much wine, then he should recite Havdalah , taste a sip of the wine, and then give it to another person who can drink melo lugmav. He should inform that person beforehand that he should have in mind when listening to the blessing of boreh peri hagefen that he will drink from the cup afterward.
- if someone is not sure whether or not he will have wine available for Havdalah, he should listen to the cantor recite Havdalah in the synagogue, but he should stipulate in his mind that he wishes to fulfill his obligation only if he has no wine at home, but that if he does find wine at home he does not wish to fulfill his obligation in the synagogue. Then, if he finds that there is wine available at home, he may recite Havdalah for himself in accordance with the condition he made. 
Wine or other drinks
- If one has wine, wine has precedence over any other drink. 
- If one doesn't have wine, one should use Chamar Medina, such as beer or cognac, but one may not use soda, coffee, tea, orange juice, lemonade, or water for Havdalah.
Saying Havdalah early
- If one is has an extreme need such as a need to travel to the end of the Techum for the purpose of a mitzvah after Shabbat one may pray Arvit starting from Plag Mincha (ten and three quarter hours into the day). In such a case one may also say Havdalah early but one may not say the Bracha on the candle (Moerei HaEsh). Even in such a case it is certainly forbidden to do Melacha (activity which is forbidden on Shabbat) until Tzet HaKochavim. 
Standing or Sitting for Havdalah
- According to Sephardim, one should sit during Havdalah. However, the Ashkenazic minhag is to stand during Havadalah. 
Doing work before making Havdalah
- Before one says Havdalah, one may not doing any Melacha. If one made Havdalah in Tefillah, one may do Melacha. If one needs to do Melacha before saying Havdalah in Tefillah, one should say "HaMavdil Ben Kodesh LeChol" (which is not a bracha) and then do Melacha. However, one may not eat until one made Havdalah over a cup of wine.
- It is permissible to use a non-religious Jewish taxi driver on Motzei Shabbat even though the taxi-driver didn't make Havdalah.
- Rambam (Hilchot Shabbat 29:1) writes that the command of "Zachor Et Yom HaShabbat" (Shemot 20:7) includes the positive mitzvahs of Kiddish and Havdalah every week. Other Rishonim that agree with Rambam include Ravi’ah Brachot 3:1, Ritvah as quoted by the Nimukei Yosef Pesachim 55, and Sefer Hachinuch Mitvah 31. However, Tosfot (Tosfot Nazir 4a s.v. My Hee in name of Rabbenu Tam) and the Rosh (Sh"t 11:3) hold that Havdalah is Derabbanan. Mishna Brurah 296:1 quotes both opinions and adds that if one said Havdalah in Tefillah the Havdalah on the wine is certainly Derabbanan.
- Mishna Chullin 26b, Gemara Shabbat 114b, Rambam Shabbat 5:21 and 29:18, S"A 491:1
- S"A 491:1, Mishna Brurah 491:1
- Sh"t Yechave Daat 4:27. Rambam (Hilchot Shabbat 29:1) writes that the Havdalah is a positive command just like Kiddish. Maggid Mishna (Hilchot Shabbat 29:1) implies from the Rambam that women are obligated in Havdalah just like they are obligated in Kiddish. Maggid Mishna suggests that even according to those who argue on the Rambam, women can be obligated if the rabbis instituted Havdalah to be just like Kiddish. Orchot Chaim (Hilchot Havdalah 18; quoted by Bet Yosef 296:8) writes that because there's a dispute whether women are obligated women shouldn't make Havdalah for themselves. Nonetheless, S"A 296:8 rules as Stam (anonymous opinion) that women are obligated in Havdalah.
- The Rama 296:8 states that women shouldn't recite Havdalah for themselves. The Bach argues that for Ashkenazim there is an additional reason to permit women to make the bracha considering that Ashkenazim allow one to make a bracha even for Mitzvot that one is not obligated in such as lulav. Magen Avraham 296:11 agrees. Mishna Brurah 296:35 concludes that a woman should not recite Havdalah for herself unless she can't find someone to hear Havdalah from. In 296:36 he writes that certainly a woman should recite it for herself if she can't find someone else to recite for her, or the only person available to say it for her already fulfilled his obligation. See audio shiur by Rabbi Aryeh Lebowitz.
- Sh"t Iggerot Moshe CM 2:47:2, Sh"t Tzitz Eliezer 14:43, Sh"t Yechave Daat 4:27
- Shemirat Shabbat Kihilchita 58:16
- Yalkut Yosef Dinei Chinuch Katan pg. 177
- S"A 491:2, Mishna Brurah 491:4. see Vetodienu
- S"A 296:1
- The Ashkenazic custom is to say the following text before Havdalah: הנה אל ישועתי אבטח ולא אפחד כי עזי וזמרת יה יהוה ויהי לי לישועה: ושאבתם מים בששון ממעיני הישועה: ליהוה הישועה על עמך ברכתך סלה: יהוה צבאות עמנו משגב לנו אלהי יעקב סלה: יהוה צבאות אשרי אדם בטח בך: יהוה הושיעה המלך יעננו ביום קראנו: ליהודים היתה אורה ושמחה וששן ויקר, כן תהיה לנו: כוס ישועות אשא ובשם יהוה אקרא:
- The source for the Ashkenazic text is the following: the Rama 296:1 writes that before the Bracha of Havdalah one should say Yishaya 12:2-3, Ester 8:16, Tehillim 116:13. The Aruch HaShulchan 296:8 adds 4 more pesukim after the ones in Yishaya from Tehillim 3:9, 46:8, 84:13, and 20:10. He also adds that after Ester 8:16 one should say 'כן תהיה לנו'.
- The Sephardic custom is to say the following text before Havdalah: כוס ישועות אשא ובשם ה' אקרא: אנא ה' הושיעה נא אנא ה' הצליחה נא: הצליחנו הצליח דרכינו הצליח לימודינו וכו' ושלח ברכה רוחה והצלחה בכל מעשה ידינו כדכתיב ישא ברכה מאת ה' וצדקה מאלהי ישענו: ליהודים היתה אורה ושמחה וששק ויקר: וכתיב ויהי דוד לכל דרכיו משכיל וה' עמו, כן יהיה עמנו תמיד: ונח מצא חן בעיני ה', כן נמצא חן ושכל טוב בעיני אלוקים ואדם: אלהא דמאיר עננו: ואתם הדבקים בה' אלוקיכם חיים כולכם היום:
- The source for the Sephardic text is the following: Yalkut Yosef (Shabbat, vol 1, pg 449-50) writes that the Sephardic minhag is to say the following order before Havdalah: Tehillim 116:13, 118:25, a prayer beginning with הצליחנו and ending with a Tehillim 24:5, Ester 8:16, Shamuel (vol 1, 18:14), Beresheet 6:8, a prayer beginning with אלהא דמאיר, and Devarim 4:4.
- Yalkut Yosef, Siman 295, Halacha 1
- Yalkut Yosef, Siman 295, Halacha 2
- Yalkut Yosef, Siman 295, Halacha 3
- Yalkut Yosef, Siman 295, Halacha 4
- Mishan Brurah 296:8
- S"A 296:2 writes that one may make Havdalah on beer if it is Chamar Medina or other drinks besides for water. Birkei Yosef 296:3 clarifies that the Shulchan Aruch's language of "or other drinks" didn't mean to include milk and oil, but rather he meant other types of Chamar Medina and exclude water even if the people of the town only drink water. Sh"t Igrot Moshe 2:75 rules that soda is just like water, isn't Chamar Medina, and thus, can not be used for Havdalah. Sh"t Vayan Avraham (Izrael) Siman 34 (pg 63) writes that he remembers in the holocaust the question arose whether lemonade could be used for Havdalah and he concludes that it just like water and can’t be used for Havdalah. Yalkut Yosef 296:8 writes that one may not use coffee, tea, orange juice, or soda for Havdalah, but one if there's no wine in the city, one may use beer or cognac which are considered Chamar Medina.
- S”A 293:3
- Tosfot 43a writes that to be included in Kiddish one should sit and then asks on those who stand during Havadalah because of the same issue. Therefore, S"A 296:6 rules that one should sit during Havdalah. However, Rama 296:6 and the Gra (Maaseh Rav pg 103, #150) write that the Ashkenazic practice is to stand for Havdalah. Mishna Brurah 296:27 explains that the reason for the Ashkenazic minhag is to escort the Shabbat queen out and escorting must be done standing. He adds that one can fulfill the obligation of others even when standing because everyone is assembled expressed for that purpose and has Kavana to fulfill their obligation. Rav Moshe Feinstein (Teshuva Siman 3 quoted in back of Radiance of Shabbos) writes that his personal minhag was to sit like his father's minhag but because of the rishonim who hold that one may stand one should not change one's minhag.
- S"A 299:10. Rav Schachter (Eretz HaTzvi p. 57) permits preparing the wine for Havdalah because Hachana isn’t considered a Melacha and may be done after Shabbat before Havdalah.
- Mishna Brurah 299:1
- Sh"t Tzitz Eliezer 12:37 writes that saying "Have a good week" does not fulfill the mitzvah of Havdalah. Sh"t Tzitz Eliezer 11:34 and 12:38 writes that there's no an issue of asking an non-religious Jew to do work for him after Shabbat since they aren't going to say Havdalah anyway, the prohibition not to do work before Havdalah doesn't set in. Rabbi Mansour on dailyhalacha.com explains this ruling. See also Rabbi Aryeh Lebowitz on yutorah.org.