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Havdalah Workshop
What's the source for saying Havdallah?

The Mishneh Torah is a legal compendium written by Rambam/Maimonides in the 12 cent.

(א) מִצְוַת עֲשֵׂה מִן הַתּוֹרָה לְקַדֵּשׁ אֶת יוֹם הַשַּׁבָּת בִּדְבָרִים שֶׁנֶּאֱמַר (שמות כ ח) "זָכוֹר אֶת יוֹם הַשַּׁבָּת לְקַדְּשׁוֹ". כְּלוֹמַר זָכְרֵהוּ זְכִירַת שֶׁבַח וְקִדּוּשׁ. וְצָרִיךְ לְזָכְרֵהוּ בִּכְנִיסָתוֹ וּבִיצִיאָתוֹ. בִּכְנִיסָתוֹ בְּקִדּוּשׁ הַיּוֹם וּבִיצִיאָתוֹ בְּהַבְדָּלָה:

(1) It is biblically mandated positive commandment to express the sanctity of the Sabbath day in words, for it is written: "Remember to sanctify the Sabbath day" (Exodus 20:8); that is to say, remember it in terms of praise and sanctification. One should remember it at its beginning and its conclusion by reciting the Kiddush when the Sabbath begins and the Havdalah when it ends.

What's the liturgical text and choreography for Havdalah?

(א) הִנֵּה אֵל יְשׁוּעָתִי אֶבְטַח וְלֹא אֶפְחָד כִּי עָזִּי וְזִמְרָת יָהּ יי וַיְהִי לִי לִישׁוּעָה:

(ב) וּשְׁאַבְתֶּם מַיִם בְּשָׂשׂוֹן מִמַּעַיְנֵי הַיְשׁוּעָה:

(ג) לַיי הַיְשׁוּעָה עַל עַמְּךָ בִרְכָתֶךָ סֶּלָה:

(ד) יי צְבָאוֹת עִמָּנוּ מִשְׂגָּב לָנוּ אֱלֹהֵי יַעֲקֹב סֶלָה:

(ה) יי צְבָאוֹת, אַשְׁרֵי אָדָם בֹּוטֵחַ בָּךְ:

(ו) יי הוֹשִׁיעָה, הַמֶּלֶךְ יַעֲנֵנוּ בְיוֹם קָרְאֵנו:

(ז) לַיְּהוּדִים הָיְתָה אוֹרָה וְשִׂמְחָה וְשָׂשֹׂן וִיקָר:

(ח) כן תהיה לנו:

(ט) כּוֹס יְשׁוּעוֹת אֶשָּׂא וּבְשֵׁם יי אֶקְרָא:

There is a custom to overflow the cup with wine, thereby to depict bountiful Divine blessings, as Psalm 23 ("Cosi revaya/My cup runneth over...") refers to. Hold the cos/cup of wine in your right hand/side of chesed/compassion and recite:

1) Here is G?d my savior, I will trust and not be afraid. For Hashem i smy might and Divine strength and will be my redemption.

2) And you will draw water in joy from the wellsprings of salvation.

3) Salvation is Hashem's Your blessings upon Your people, selah (yay).

4) Abundant Hashem is with us. The G?d of Yaakov is our fortress, selah.

5) Abundant Hashem, happy is the one who trusts in You.

6) Hashem will save, the Ruler will answer us as soon as we call/say "YES!"

7) The Jews had light, joy, jubilation and glory.

8) So too for us:

9) I will raise the cup of redemption and call out in Hashem's name.

(translation by David Zvi Kalman, Sarah Wolf and Joshua Schwartz)

This is minhag/custom Ashkenaz. The source for the Ashkenazic text is the following: the Rama/Moshe Isserles, a 16th cent. authority in Jewish law from Poland, 296:1 writes that before the Brocho/blessing of Havdalah one should say Yishaya/Isaiah 12:2-3, Ester 8:16, Tehillim/Psalms 116:13.
The Aruch HaShulchan/Yechiel Michel haLevi Epstein, a 19th cent. authority in Jewish law from Lithuania, 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/ken t'hiyeh lanu.
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, written by R' Yitzchok Yosef based on the rulings of his father, a gadol/big deal authority of Jewish law, R' Ovadia 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, Shmuel/Samuel (vol 1, 18:14), Beresheet/Gen 6:8, a prayer beginning with אלהא דמאיר, and Devarim/Deut 4:4.
(Taken from: https://www.halachipedia.com/index.php?titl=Havdalah)

בָּרוּךְ אַתָּה יי אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם, בּוֹרֵא פְּרִי הַגָּפֶן:

בָּרוּךְ אַתָּה יי אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם, בּוֹרֵא מִינֵי בְשָׂמִים:

בָּרוּךְ אַתָּה יי אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם, בּוֹרֵא מְאוֹרֵי הָאֵשׁ:

בָּרוּךְ אַתָּה יי אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם, הַמַּבְדִּיל בֵּין קֹדֶשׁ לְחוֹל, בֵּין אוֹר לְחֹשֶׁךְ, בֵּין יִשְׂרָאֵל לָעַמִּים, בֵּין יוֹם הַשְּׁבִיעִי לְשֵׁשֶׁת יְמֵי הַמַּעֲשֶׂה, בָּרוּךְ אַתָּה יי, הַמַּבְדִּיל בֵּין קֹדֶשׁ לְחוֹל:

Still holding the cos, say:

Blessed are You, LORD our God, King of the Universe, who creates the fruit of the vine.

[Put the cos down. The person reciting Havdalah does NOT drink the grape juice yet.]

Lift up the spice box and say:

Blessed are You, LORD our God, King of the Universe, who creates the various spices.

[The spices are passed around for everyone to smell]

Elevate the candle for everyone to see and say:

Blessed are You, LORD our God, King of the Universe, who creates the lights of fire.

[At this point, many have the custom to hold their fingernails to the flame so that the light reflects off them.]

Pick the cos back up in your right hand and say:

Blessed are You, LORD our God, King of the Universe, who distinguishes between sacred and secular, between light and darkness, between Israel and the nations, between the seventh day and the six days of labor. Blessed are You, LORD, who distinguishes between sacred and secular.

[At this point, the flame is put out (many do so by dipping it in spilt wine/grape juice), and the person who said Havdalah drinks the wine/grape juice. Many also have the custom of dipping their pinkies in the spilled wine and touch their wine-covered pinkies to their eyes to embody a desire to be guided by the light of the mitzvah, touch to behind the ears to embody hearing only good news, the back of the neck to invoke protection and to the pockets to invoke an influx of parnassa/monetary resources.]

According to Rabbi David Abudraham (the author of a medieval commentary on the liturgy), the reason for smelling spices at Havdalah comes from the following source:

דאמר ר' שמעון בן לקיש נשמה יתירה נותן הקב"ה באדם ערב שבת ולמוצאי שבת נוטלין אותה הימנו שנאמר (שמות לא, יז) שבת וינפש כיון ששבת ווי אבדה נפש:
As Rabbi Shimon ben Lakish said: The Holy One, Blessed be He, gives a person an additional soul on Shabbat eve, and at the conclusion of Shabbat removes it from him, as it is stated: “He ceased from work and was refreshed [vayinafash]” (Exodus 31:17). Rabbi Shimon ben Lakish expounds the verse as follows: Since he ceased from work, and now Shabbat has concluded and his additional soul is removed from him, woe [vai] for the additional soul [nefesh] that is lost.

According to many commentators, the following talmudic legend is the reason for reciting a blessing on fire with Havdalah:

אלא חללה קודם שנברא העולם ואור דידיה בשני בשבת ואור דידן במחשבה עלה ליבראות בערב שבת ולא נברא עד מוצאי שבת דתניא רבי יוסי אומר שני דברים עלו במחשבה ליבראות בערב שבת ולא נבראו עד מוצאי שבת ובמוצאי שבת נתן הקדוש ברוך הוא דיעה באדם הראשון מעין דוגמא של מעלה והביא שני אבנים וטחנן זו בזו ויצא מהן אור

And the thought arose in God’s mind to create our fire on Shabbat eve; however, it was not actually created until the conclusion of Shabbat, as it was taught in a baraita/source outside of the Mishnah that Rabbi Yosei says: The thoughts of two phenomena arose in God’s mind on Shabbat eve, but were not actually created until the conclusion of Shabbat. At the conclusion of Shabbat, the Holy One, Blessed be He, granted Adam, the first man, creative knowledge similar to divine knowledge, and he brought two rocks and rubbed them against each other, and the first fire emerged from them.

It is customary to hold one's fingernails up to the flame. The following source is one reason given for this practice:

אין מברכין על הנר עד שיאותו לאורו:

We do not bless over the flame until its light is used/benefitted from.

The Mishnah Brurah is a commentary to the Shulchan Arukh written Rabbi Yisrael Meir Kagen, who lived in the 20th century in Eastern Europe. First, he explains that we hold up our fingernails to benefit from the light. However, the then provides a more symbolic explanation:

...ועוד שהצפרנים הן סימן ברכה שהן פרות ורבות לעולם...

Also because the fingernails are a sign of blessing, since they always grow [literally, that they are fruitful and multiply forever].