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1. When was the first Shavuos Holiday celebrated?
The Holiday of Shavuos was celebrated for the first time 51 days after we left Egypt. [Accordingly, it was celebrated during the forty-year period that the Jews wandered in the desert, and was not delayed until we entered Eretz Yisrael.]
2. Is Shavuos a Biblical or Rabbinical Holiday during times of exile?
According to all opinions, the Holiday of Shavuos is considered a Biblical Holiday during all times, including times of exile. This applies even though the Mitzvah of Sefiras Haomer is no longer of Biblical status according to most Poskim. Although the Torah states that Shavuos falls on the 50th day of the count, nonetheless, it is not dependent on the physical count, or the Mitzvah of the count, but simply on the physical passing of 50 days from the 16th of Nissan, irrelevant to whether one counted or not, and irrelevant if one is even obligated in counting at all.
3. On what weekdays can Shavuos fall on?
The first day of Sivan can fall on a Sunday, Tuesday, Wednesday, and Friday. It cannot fall on Monday, Thursday, Shabbos. Accordingly, the first day of Shavuos, the 6th of Sivan, can only fall on Sunday, Monday, Wednesday, and Friday. It cannot fall on Tuesday, Thursday, and Shabbos. The second day of Shavuos in the Diaspora can fall on Monday, Tuesday, Thursday, Shabbos.
4. Was the Torah given on Shavuos?
No! The first Shavuos Holiday was in fact celebrated the day before Matan Torah, as the Torah was given on Shabbos, the 51st day of the Omer, while Shavuos that year fell on Friday, the 50th day of the Omer. Nonetheless, the Holiday of Shavuos has become synonymous with the commemoration of Matan Torah in culture as well as in various matters of Halacha and Minhag, such as the prohibition to fast according to all opinions, reciting Zeman Matan Toraseinu in prayer, reading the section of the Aseres Hadibros in Kerias Hatorah, beautifying one’s home with flours and plants, staying awake throughout the night learning, eating dairy. The reason for this is because the Torah was given on the 6th day of Sivan, and in today’s calendar the 50th day of Sefira always coincides with the 6th of Sivan. Furthermore, there is also an internal connection between Shavuos, which is the 50th day of the Omer, and Matan Torah, as the Torah is fit to be received on the 50th day of preparation of Sefira. [See Shaar Halacha Chapter 1 for the full details on this matter.]
6. Where was the Torah given?
The Torah was famously given on the mountain called Har Sinai or Har Choreiv. The tradition of its location became lost with the generations, and its last recorded whereabouts is recorded in Sefer Melachim regarding Eliyahu’s escape into a cave in the feet of the Sinai mountain. There is a tradition recorded in Poskim that the Sinai mountain contains a bush shaped rock [see next], although it is unclear where this mountain is found. Various non-Jewish traditions as to the location of this mountain have surfaced over the centuries, although none have conclusive evidence to provide to verify the location. Traditions, and historical speculation, vary from the Jebel Musa mountain in the Sinai Peninsula, to the Jabel Al Luz mountain in Saudi Arabia, all the way to the Kilimanjaro mountain in Tanzania. Practically, we do not have a tradition in this matter and any one of thousands of mountains in the Sinai and Arabian Peninsula can potentially be the Sinai mountain.
7. The bush shaped rocks of the Sinai mountain?
Some Poskim record that the reason that the mountain is called Sinai is because the word Sneh means bush. The reason why this mountain is called “bush” is because the rocks of this mountain contain a natural phenomenon, no less than a miracle, in that every piece of its rock contains the picture of a bush. No matter how many times one breaks a piece of its rock he will see a form of a complete bush within the rock.
8. Why were such simple and self-understood commands given by Matan Torah?
On Sinai we were given the Ten Commandments, which included laws such as to honor one’s parents, not to murder, not to steal, not to commit adultery. These commands are seemingly obvious, and self-obligatory, and have been accepted in all parts of civilization as binding, irrelevant of Matan Torah. Some of them were already part of the Seven Noahite laws which are binding on all human beings, and were already kept prior to Matan Torah. Why then did Hashem choose Matan Torah to repeat these commands? The reason for this is because Hashem wanted to show that even such commands must be fulfilled solely due to the fact that G-d commanded us and not due to the intellectual understanding to do so. This is the fundamental principal of Kabbalas Ol. Alternatively, the reason is because the purpose of Matan Torah is to connect the upper and lower worlds, and make a dwelling place for G-d below, and hence G-d’s will had to penetrate even the most lowly of matters, such as murder, stealing and adultery.
9. Why did Hashem give the Torah specifically on Har Sinai versus the other mountains?
When the Torah was given, many mountains offered their services to have the momentous event transpire on their grounds. Only one mountain was chosen, and that is the famed mountain of Sinai. The Sinai Mountain contrasted from other mountains physiologically, in that it was small, not reaching to very great heights as did the other mountain, such as Mount Tabur, Mount Carmel or Mount Hermon. Nonetheless, specifically the Sinai Mountain was chosen to have the Torah given. This was due to the following reason: Height represents haughtiness which is the root of all evil and is the antithesis of Torah, as Torah can only grasped through humility. On this the Sages state [Eiruvin 54a] “If one makes himself like a desert which all step on, the Torah can be established within him”, which means that if one learns Torah with humility, without haughtiness, then the Torah can internalize within him. This is also why in prayer we first say “Venafshi Keafar Lakol Tihyeh/ May my soul be like dust before all” and only then do we say “Pesach Libi Besorasecha/Open my heart to your Torah.” For this reason, the Torah was not given on the high mountains, as they represent a high level of ego. Har Sinai on the other hand was low, which represents humility.
Why did Hashem give the Torah specifically on Har Sinai versus a valley or flat land? Based on the above it remains to be understood why at all a mountain was chosen for the giving of the Torah. If the lower you are the more humility you represent, then would it not have been fitting to give the Torah on plain land, or a valley? The explanation is as follows: Although Torah requires Bittul, self-subjugation of the ego, it nevertheless also requires a feeling of self-confidence, that one feels assured that he is able to serve G-d and stand up to his evil inclination and battle it. Therefore the Torah was given on Har Sinai which contained a minimal height, as it represents a balanced ego; an ego which is humble enough to preserve the Torah and at the same time have the self-respect to stand up for the good and battle the evil. This is why the mountain was called Har Sinai, which can also mean the mountain of hatred, as it brought hatred and enmity to the Kelipos, as through this form of service one is able to battle his evil inclination.
Shavuos is the day that we accepted the Torah. This represents the level of Keser. Keser is a single unit which is above the 7 attributes and thus the festival is not split to seven days.
 See Admur 468:22 “As on the day of Shavuos, before Matan Torah, a spirit called Tavuach came and said that if the Jewish people do not accept the Torah he will slaughter them, their blood and flesh. Therefore, there is an everlasting danger in every generation to let blood on this day, which is Erev Shavuos.”; See Admur 494:1 that in the year of the exodus, Matan Torah was on the 51st day of count, which would make Shavuos, the 50th day, fall on Erev Matan Torah.”; See Shabbos 129b; M”A 468:15
Background: From one viewpoint, being that the Holiday of Shavuos is dependent on the counting of Sefira which is itself dependent on the Omer and Shtei Halechem, one can argue that the Holiday of Shavuos did not become obligatory until after the Jewish people entered into Eretz Yisrael and were able to bring the Omer on the 16th of Nissan of that year. [See Yalkut Behar that the Omer was first brought on the 16th of Nissan a few days after entering Eretz Yisrael, and not beforehand during the 40 years in the desert; The Shtei Halechem was first offered that Shavuos. See also Toras Menachem 1991 3:95, brought in Shulchan Menachem 3:9] Nonetheless, it is clear from the Poskim ibid, that Shavuos was celebrated 51 days after we left Egypt. One must hence conclude that Shavuos is not dependent on the fulfillment of the Mitzvah of Sefira. See next footnote
 Setimas Kol Haposkim! Likkutei Sichos 3:997 [Printed in Shulchan Menachem 3:20-21]
Background: From to one viewpoint, being that the Holiday of Shavuos is dependent on the counting of Sefira which is itself dependent on the Omer and Shtei Halechem, one can argue that during exile the festival of Shavuos is only of Rabbinical, status, as we no longer bring the Omer or Shtei Halechem offering. This however is factually incorrect, as no Posek has ever made such a differentiation, or suggestion, that during exile the festival of Shavuos is Biblical. There are various ramifications the first and second day of Yom Tov, and if the first day of Yom Tov was only Rabbinical, mention would have been made. Hence, it is clear that everyone agrees Shavuos is a Biblical Holiday by all times. Furthermore, according to this view women would not be obligated in the Mitzvah of Shavuos, as it is dependent on the count, and they are exempt from counting.
 See Michaber 428:1-3; Rambam Kiddush Hachodesh 7; Our Sefer on “The laws of Rosh Chodesh”
 Admur 468:22 “As on the day of Shavuos, before Matan Torah…” [See Shabbos 129b; M”A 468:15]; Admur 494:1 that in the year of the exodus, Matan Torah was on the 51st day of count, which would make Shavuos, the 50th day, fall on Erev Matan Torah.”; M”A 494:1; Chok Yaakov 494:1; See Aruch Hashulchan 494:1
 Admur 494:1; Rivash 96; Peri Chadash 494:1; Chok Yaakov 494:1; See Likkutei Sichos 3:997
 See Likkutei Sichos 3:997; The Divrei Nechemia Hashlamos 581 Kuntrus Acharon suggests that the reason we say Zeman Matan Toraseinu in Davening, and connect Shavuos with Matan Torah is because in truth the Torah was meant to be given on the 50th day of the Omer, which is the Shaar Hanun of Bina, and it is due to alternative factors that in the first year the giving of the Torah was delayed until the next day. Accordingly, each year, on the 50th day of the Omer, the revelations of Matan Torah take effect irrelevant to the day of the month, and therefore even if Shavuos falls on the 5th or 7th of Sivan one is to say Zeman Matan Toraseinu. The Rebbe ibid negates his opinion, although explains that there are two aspects of Matan Torah, one personal and the second global. The personal Matan Torah is on one’s 50th day of count, irrelevant of the date of the month. The global Matan Torah however only takes place on the 6th of Sivan each year, irrelevant to one’s day of count. The personal Matan Torah represents that time that one is fit to receive the Torah while the global Matan Torah represents when Hashem actually gives the Torah.
 Yaavetz in Migdal Oz p. 240
 Yaavetz in Migdal Oz p. 240
 Likkutei Sichos 3:889
 Hisvadyus 5750:274
 Likkutei Torah Bamidbar p. 15
 Likkutei Torah Bamidbar p. 15