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The day after each of the three Holidays is called Isru Chag. The name Isru Chag derives from the verse “Isru Chag Baavosim Ad Karnei Hamizbeiach”. This means to say that this day is to be attached [i.e. Isru] to the Holiday itself, and by doing so the verse considers one to have built an Altar and sacrificed on it an offering. For this reason, the following customs are relevant on Isru Chag:
Increasing in eating and drinking on Isru Chag:
One is to increase a little in eating and drinking on Isru Chag, the day after each of the three festivals.
Fasting on Isru Chag:
Chasan and Kallah: Even a Chasan and Kallah which are getting married on Isru Chag may not fast that day. Yartzite: A son/daughter may not fast on his parent’s Yartzite that falls on Isru Chag.
One is to increase a little in eating and drinking on Isru Chag. Even a Chasan and Kallah on the day of their wedding may not fast on this day. Similarly, a son/daughter may not fast on his parent‘s Yartzite.
Do the customs of Isru Chag apply also on the night after [i.e. Motzei] Isru Chag?
Is one to wear Shabbos clothing on Isru Chag?
Sparks of Kabbalah:
The Arizal taught that on the day after Yom Tov, Isru Chag, a ray of the Holiday still shines.
 Admur 429:17
 Admur 429:17; Sukkah 45b
 Admur ibid; Rama 429:2
 Admur 429:17; Rama 429:2; Sukkah 45b based on second explanation of Rashi ibid [according to his 1st explanation, the Mitzvah is to increase on Yom Tov itself, and not the next day]
 The reason: Anyone who attaches [Lit. Issur which means bound] the day after the festival to the festival itself with eating and drinking, meaning through increasing slightly in eating and drinking the day after the Holiday, and thus makes that day attached [Lit. Tafal which means secondary, or attached] to the Holiday itself, the verse considers him to have built an Altar and sacrificed on it an offering. This is based on the verse that states “Isru Chag Baavosim Ad Karnei Hamizbeiach”. Meaning to say that when one makes an Issur, a secondary day, to the festival, then Baavosim, it is considered as if he brought large and fat animals to the altar. For this reason the custom is in these provinces to increase a little in eating and drinking on the day after each of the three festivals. [Admur ibid; Sukkah ibid]
Other reasons: Some write that the celebration of Isru Chag began in Eretz Yisrael in order to show some sign of festivity on the second day of the festival of the Diaspora. This then spread to the Diaspora itself, on their Isru Chag. Alternatively it corresponds to the sacrifices which were able to be eaten for two days and one night. [Sdei Chemed Kelalim Alef 154] Alternatively it is in memory of the pilgrimage which would return home on Isru Chag. [Glosses of Chasam Sofer 429]
 Admur 494:19; 429:17; Michaber 494:3; M”A 429:8; Igur 665
A Taanis Chalom: It is certainly permitted to fast a Taanis Chalom on Isru Chag, as even on Shabbos it is permitted. Nevertheless Tzaruch Iyun if such a fast requires a second fast as a Kaparah.
 From the letter of the law it is forbidden to fast on Motzei Shavuos. This is opposed to other holidays in which the prohibition of fasting on their Isru Chag is only a custom, as explained in 429:17
The reason: The reason it is forbidden from the letter of the law to fast on Isru Chag of Shavuos is because this day was a day of sacrifices [Yom Tavuach] in the times of the Temple. On this day all the sacrifices of the pilgrimage [Olas Ri’iyah] were offered in the Temple, [and it was thus made a festival]. These sacrifices were not able to be offered on Yom Tov itself, being that they have no need of Ochel Nefesh [as the entire sacrifice was consumed by the fire and was not eaten]. One may therefore not desecrate Yom Tov on their behalf being that it is possible to offer them after Yom Tov, as the sacrifices of Shavuos may be offered as Tashlumin up until seven days after Shavuos. Now, although this was the opinion of Beis Shamai while according to the opinion of Beis Hillel it is permitted to offer the Karban even on Yom Tov itself. Nevertheless, even Beis Hillel in actuality performed like the ruling of Beis Shamai [see Likkutei Sichos 28:26 footnote 26; however see Kuntrus Hashulchan ibid], and hence many did not bring their sacrifices on Yom Tov but rather after Yom Tov. This day of Motzei Yom Tov hence became for them like a Yom Tov which is forbidden in Hesped and fasting. Now, [since for most Jews Motzei Yom Tov was a Holiday as it was the day of their Karban] therefore even today after the destruction of the Temple [it remains a Holiday and] contains a prohibition of fasting and eulogies. However, on Isru Chag of Sukkos/Pesach it was not a day of sacrifices [Yom Tavuach] even according to Beis Shamai, as all the Karbanos Reiyah were sacrificed on Motzei Yom Tov Rishon which is Chol Hamoed, [and hence on Isru Chag there were no Karbanos that were brought]. Therefore, on their Isru Chag there is no prohibition from the letter of the law against fasting and it is merely a custom to treat the day as a holiday, as explained in 429:17. [Admur 494:19; See Mishneh Chagiga 17a]
 The above prohibition is only a custom, however from the letter of the law there is no prohibition to fast, although one who refrains from doing so is praised. [Admur ibid; M”A 429:8]
 Admur 429:17; M”A 573:1 regarding Isru Chag of Pesach and Sukkos, which is only a custom, and certainly it applies to Isru Chag of Shavuos which is considered a Holiday from the letter of the law.
 Admur ibid; Rama 429:2 regarding all days of Nissan; See also Rama 568:9
 Ashel Avraham of Butchach 429
 The reason: As this is similar to Kodshim in which the night follows the day in terms of the burning of the offerings from the sacrifice. [ibid]
 Torah Leshma 140; Darkei Chaim Veshalom 524
 The reason: This is done in order to actively show the continuity of Holiness of the festival that is relevant to this day, and is also done so one does not treat it like a regular weekday. [Torah Leshma ibid]
 Torah Leshma 140