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The following is an explanation of the Nussach that we recite in the Siddur.
Hallelukah: The Shlah records a tradition to recite the Psalm Hallelukah Halilu Keil Bekadsho.
Siman Tov: One recites “Siman Tov Tihyeh Lechol Yisrael, Baruch Yotzreich” three times.
Kisheim Sheani Rokeid: One recites “Ksheim Sheani Rokeid..Tipol Aleihem…” One then says it backwards “Kaeven Yidmu”. [One recites Baruch Oseich etc corresponding to the three worlds of Asiya, Yetzira and Beriyah. This is done in order to save the worlds from the Kelipos. Between each world there is a skipping of a level, therefore we dance three times.]
David Melech Yisrael Chaiy Vekayam: The custom is to recite David Melech Yisrael Chaiy Vekayam. The reason why we mention King David is because his kingdom is a parable of the moon, as just as the moon renews each month, so too his kingdom will become renewed in the future. Now, just as the moon each month greets the sun light and hence is renewed, so too the Jewish people will in the future return to attach to G-d.
Reciting Shalom Aleichem: One is to greet a friend three times with the words Shalom Aleichem. [This means that one greets three friends with the words Shalom Aleichem. If there are not three people available one is to say it to himself.] The person who was asked Shalom Aleichem is to reply Aleichem Shalom. One who answers Aleichem Shalom to his friend is considered as if he asked him Shalom Aleichem.
Kol Dodi: It is a tradition from Rav Yehuda Hachassid to recite “Kol Dodi…” until “Meitzitz Min Hacharakim.”
Shir Hamaalos Esa Eiynaiy: The Shlah records a tradition to recite Shir Hamaalos Esa Eiynaiy, Tana Divei Reb Yishmael and Veamar Abayeiy.
Kaddish Derabanan: The Shlah records a tradition to recite Kaddish Derabanan at the conclusion of Kiddush Levana. However Admur in the Siddur records to recite Kaddish Yasom and so is the Chabad custom.
Reciting Al Tira:
In certain Chabad Siddurim the verses of Al Tira were placed to be recited after Kiddush Levana. It requires further analysis as to the source for this addition. Many Chabad Siddurim lack this addition. To note the Rebbe did not add the verses of Al Tira in the compilation of the blessing of the sun which follows a similar pattern to that of the blessing of the moon.
Reciting Ana Bekoach:
In the first printing of the Siddur it was written to recite Ana Bekoach at the conclusion of the Psalm of Lamnatzeiach. In later prints this addition was omitted. The Shaar Hakolel suggests the reason for its omission is because Ana Bekoach is only said to elevate from below to above while Kiddush Levana, which is like receiving the Shechina, is a drawing down from above to below.
If one is saying Kiddush Levana by himself, is he to search for people to ask them Shalom Aleichem?
The custom is to do so.
Why is the blessing of Shehechiyanu not recited over Kiddush Levana?
Various answers are suggested:
- As in order to recite Shehechiyanu there must be a break of 30 days between the two Mitzvos, and since at times there is only 29 days in between the two times, therefore Shehechiyanu is not recited.
- As the entire blessing of Kiddush Levana is on the renewal of the moon.
 M”A 426/10
 Michaber ibid
 Rama ibid
 Shaar Hakolel 33/5
 Rama ibid
 Rama ibid
 The reason for saying Shalom Aleichem: As earlier one said “Fear and trepidation shall fall upon you..” therefore one assures his friend that to him there will be peace. [Perisha 426] Alternatively, it is said being that all those present merited receiving the Shechina. [Levush 426/2] Alternatively, it is said because Hashem sends down angels to us who are called Shalom. [Peri Eitz Chaim] Alternatively, it is said towards the moon who was diminished and we hence now bless it that it will no longer be prosecuted. [Mishnes Chassidim; Shaar Hakolel ibid]
The reason it is said in plural: It is said in plural as according to the Mekubalim its intent is towards the angels who escort every person. [Shaar Hakolel 33/7]
 Mateh Moshe 540; See Levush 426/1 “…If there are two or three people saying it together then one greets them with Shalom”. Thus, the wording of friend is not to be understood to mean one tells the same person Shalom Aleichem three times; See also Kuntrus Inyanei Tefila of Gra”ch Naah, printed in Yagdil Torah Tzemach Tzedek 17/16
 Shaar Hakolel 33/7; See however Levush in previous footnote that this is negated.
 Siddur Admur
The reason: Shaar Hakolel ibid explains one must answer back Aleichem Shalom as the Gemara in Brachos 6b states one who is greeted with Shalom and does not reply it is considered as if he stole the blessing. According to the Mekubalim, there is no need for the person being asked to answer back Aleichem Shalom as it is being said towards the angels.
 Rama ibid
 Mateh Moshe 541, brought in Kaf Hachaim 426/44
 M”A 426/10
 Siddur; See Kaf Hachaim 426/47
Other opinions: Some Poskim discourage the saying of Aleinu Lishabeiach after Kiddush Levana. [Moreh Baetzba 190] Others defend the practice. [See Kaf Hachaim 426/47]
 The reason: This is said to emphasize that we are praying to Hashem and not to the moon. [Biur Halacha 426 “Umivareich Meumad”] Alternatively, the reason for saying Aleinu Leshabeiach is because it was authored by Yehoshua who is compared to the moon. [Elya Raba 132/3 brought in Taamei Haminhagim 463]
 Shlah Shaar Osiyos Os Yud brought in Kaf Hachaim 426/44
 The reason: The reason for saying Kaddish is in order to complete G-d’s name, which will effect that the light of the moon will be like the light of the sun. [Shlah Shaar Osiyos Os Yud]
 See Glosses of Rav Raskin on Siddur p. 364; Rabbi Groner replied to me regarding whether Al Tira should be said: “I don’t know, I was never able to verify the correct way.”
 Kehos Tehilas Hashem 2004 and many other editions
 Shaar Hakolel 33/11; See Igros Kodesh 7/136 where Harav Yitzchak Dubov asked the Rebbe why Ana Bekoach is said by Kiddush Levana, and the Rebbe replied to look in Shaar Hakolel ibid. In any event it is seen that some Chassidim had a tradition to recite Ana Bekoach by Kiddush Levana.
 Kuntrus Inyanei Tefila of Gra”ch Naah, printed in Yagdil Torah Tzemach Tzedek 17/16
 Elya Raba 422/1; P”M 426 A”A 1; Abudarham Shaar 3; Kneses Hagedola 422; M”A 422/5; Kaf Hachaim 422/31
 Shibulei Haleket 167; See Kesav Sofer 34