Gemara

3b (Beraisa): If the bread was baked, the animals were slaughtered, or the wine was mixed, and then the Chasan's father or bride's mother died:

We put the deceased in a room until after the Chupah. They have Bi'as Mitzvah, and separate. They celebrate the seven days of Mishteh (nuptial festivities), followed by seven days of Aveilus.

All 14 days he sleeps among men, and she sleeps among women. She may use any cosmetics she desires during the 30 days of Aveilus.

4a: The need to sleep with others supports R. Yochanan, who says that even though we do not show signs of Aveilus during the Mo'ed (the days of Mishteh are like a Mo'ed), private matters (relations) are forbidden.

Mo'ed Katan 14b: Aveilus does not apply during the Mo'ed because it says "V'Somachta b'Chagecha". If he was an Avel before the Regel, the Aseh of the Rabim (the Regel) overrides the Aseh of an individual. If he became an Avel during the Regel, the Aseh of an individual does not override the Aseh of the Rabim.

19b (Abaye) Question: If a Mes was buried during the Regel, do the days of the Regel count towards Sheloshim (the restrictions of the 30 days of Aveilus)?

I do not ask whether or not they count towards Shivah. Since laws of Shivah do not apply during the Regel, surely they do not count.

I ask about Sheloshim, for some laws of Sheloshim apply during the Regel.

Answer (Rabah): They do not count.

Question (Beraisa): If one buried his Mes two days before a Regel, he counts five days after the Regel. Others may do his work; his slaves may work covertly in his house. Many console him during the Regel, therefore we do not do so afterwards. The rule is, the Regel interrupts things that are due to Aveilus (and he must finish the seven days afterwards), but not matters of the Rabim (consolation).

Rishonim

The Rif and Rosh (1:5): bring our Gemara.

Rosh (1:6): Rashi says that we do not withhold any cosmetics from the Kalah due to the 30 days of Aveilus. This is difficult, for Maseches Semachos teaches that the Isurim of Sheloshim, i.e. cutting hair and laundering, do not apply to any married woman lest she become repulsive to her husband. It seems that this refers to any Kalah within 30 days of the Chupah. She may use any cosmetics she desires even during Shivah, lest she become repulsive to the Chasan. Aveilus does not take effect on her regarding these things.

Korban Nesan'el (20): This is not in our text of Maseches Semachos.

Rosh (1:6): (When a parent died), after the days of Mishteh he conducts seven days of Avelus, and another 23 days for Sheloshim. This is unlike one who buried his Mes during the Regel. Such a person finishes Sheloshim 30 days from the burial, for he was forbidden to cut his hair or launder during the Regel. These are permitted to a Chasan, because "Melech b'Yafyo Techezenah Einecha", therefore the days of Mishteh do not count towards Sheloshim.

Rosh (Mo'ed Katan 3:28): Shemini Atzeres does not cancel Sheloshim when Sukos cancelled Shivah, for then he never observed Sheloshim.

Taz (YD 399:6): The Ramban says that some observances of Sheloshim apply during the Regel. Nevertheless it is not the primary observance of Sheloshim, so Shemini Atzeres does not cancel Sheloshim.

Rif and Rosh (Mo'ed Katan 11b and 3:3): If a Mes died and was buried on Yom Tov Sheni of Chutz la'Aretz at the end of the Regel or Shavu'os, since Yom Tov Sheni is mid'Rabanan and the first day of Aveilus is mid'Oraisa, an individual's Aseh mid'Oraisa overrides the Aseh mid'Rabanan.

Nimukei Yosef (DH v'Chosav): Meforshim are unsure whether or not one may tear Kri'ah on Yom Tov Sheni. Regarding others matters of Aveilus it is like a Yom Chol. Or, perhaps it is forbidden because Yom Tov Sheni is Safek Yom Tov, and one who tears on Yom Tov is liable, for this is Metaken.

Rambam (Hilchos Evel 10:3,8): Aveilus does not apply during the Regalim, Rosh Hashanah or Yom Kipur.

Beis Yosef (YD 399 DH u'Mah she'Chosav b'Shem and OC 548 DH v'Havi): It seems that the Rambam's text (Kesuvos 4a) said 'private matters apply on Shabbos'. He holds that they do not apply during the Mo'ed. Even though Shabbos should be more lenient (since we never bury on Shabbos), since Shabbos must always be part of Shivah, private matters apply. The Ramban and many others disagree; the Halachah follows them.

Gra (3): Surely the correct text says 'private matters apply during the Mo'ed'. The seven days of Mishteh are equated to Mo'ed. The Tosefta and Yerushalmi explicitly forbid private matters during the Mo'ed.

Rambam (9): Aveilus does not apply on Yom Tov Sheni.

Rambam (10): If a Mes died and was buried on Yom Tov Sheni of Chutz la'Aretz at the end of the Regel or Shavu'os, Aveilus applies. An Aseh mid'Oraisa (the first day of Aveilus) overrides an Aseh mid'Rabanan (Yom Tov Sheni). Both days of Rosh Hashanah are like one long day, so Aveilus does not apply.

Rosh (ibid.): Some say that if a man or his wife is an Avel during the Mo'ed, they must sleep separately among men and women. This is like a Chasan; since we were lenient, we added this stringency. The Ra'avad rejects this. The stringency is only for a Chasan, who has excessive Simchah. I say that the stringency of Chasan is because we were lenient to postpone burial and make Nisu'in to override Aveilus. The Mo'ed overrides Aveilus by itself.

Poskim

Shulchan Aruch (YD 399:1 and OC 548:1,6): If one buried his Mes before a Regel but did not conduct like an Avel, Yom Tov does not cancel Shivah. He observes private matters during the Regel. He is Batel from work during the Regel due to the Mo'ed, not because of Aveilus. Many console him during the Regel. The Regel counts towards 30 days, since the Isurim of laundering and cutting hair apply. This is not due only to the Mo'ed. During the Mo'ed others may wear new white laundered clothing, cut their nails with a scissors, be merry, and sometimes even cut their hair and launder, e.g. one who came from overseas or escaped captivity... All of these are forbidden to an Avel, just like on a Yom Chol.

Source (Ramban, brought in Beis Yosef YD DH u'Mah she'Chosav Ela): The Mo'ed does not count towards Shivah, since laws of Shivah do not apply. It counts towards Sheloshim, because some laws of Sheloshim apply. But also some laws of Shivah apply, e.g. he may not wash his garment even in water and people console him! We must say that all laws of Sheloshim apply, i.e. laundering and shaving, even when they are not forbidden due to the Regel. They are all Isurim, and most of them normally apply because of the Regel anyway, so it does not look like open Aveilus.

Rebuttal (R. Binyamin, brought in Taz 2): There are six primary laws of Shivah, the acronym is 'Pachaz' and 'Natar' (covering the head... (Mo'ed Katan 24a)). Laundering is not among them! Also, perhaps an Avel may wash his garment in water during the Mo'ed!

Defense (Taz): The Gemara discusses whether an Avel may fulfill 'Pachaz' and 'Natar' on Shabbos, or if this is open Aveilus. It does not mention laundering, for surely it is forbidden! Surely an Avel may not wash his garment in water during the Mo'ed, for private matters apply!

Shulchan Aruch (OC 548:1 and YD 399:2): If one buried his Mes during the Mo'ed, Aveilus does not apply to him during the Mo'ed. He observes seven days of Aveilus after the Regel.

Mishnah Berurah (3): Our custom is to light a Ner all seven days of Aveilus. An Avel may do so during the Mo'ed, but not where he eats or the Mes is, lest he come to eulogize. Since we do not benefit from the Ner, a Yisrael may not light it on Yom Tov.

Kaf ha'Chayim (3): The Rema (YD 393:4) says that an Avel does not pray in his usual place on Shabbos. The same applies during the Mo'ed, but only if he (became an Avel and) changed before the Mo'ed. The Shulchan Aruch holds that he does not change even on Shabbos, and all the more so during the Mo'ed.

Shulchan Aruch (OC 2): Aveilus does not apply on Yom Tov Sheni.

Shulchan Aruch (OC 3): If a Mes died and was buried on Yom Tov Sheni of Chutz la'Aretz at the end of the Regel, since Yom Tov Sheni is mid'Rabanan and the first day of Aveilus is mid'Oraisa, Aveilus overrides Yom Tov Sheni.

Mishnah Berurah (10,11): Aveilus is mid'Oraisa on the first day only if it is the day of death, and only for the seven relatives, but not for the mid'Rabanan additions. The Torah requires Kohanim, and all the more so Yisraelim, to become Tamei to their relatives, lest they refrain from Aveilus.

Shulchan Aruch (YD 13): Some say that Aveilus does not apply on any Yom Tov Sheni, even if it is the day of death and burial.

Rema (YD and OC): They hold that all Aveilus is mid'Rabanan. This is our custom; one should not deviate.

Shulchan Aruch (OC 4 and YD 2): Aveilus does not apply when the Mes was buried during the Mo'ed regarding open matters. It applies to private matters.

Kaf ha'Chayim (17): One may rely on those who permit learning Torah, but he should not be counted towards the required number of Aliyos.

Rema: He may be secluded with his wife.

Shulchan Aruch (OC 5 and YD 2): Aveilus does not apply, but Aninus applies.

Shulchan Aruch (OC 6): Even though Aveilus does not apply during the Regel, we console him during the Regel. Others may do his work in their houses. His slaves may work covertly in his house.

Mishnah Berurah (22): If there is Devar ha'Eved and he cannot get others to do it, he can rely on those who permit the Avel himself to do it.

Rema (YD): He himself may do any Devar ha'Eved permitted during Chol ha'Mo'ed. If it is not Devar ha'Eved, others may do it for him in their houses. His slaves may work covertly in his house.

Source: R. Yerucham, brought in Beis Yosef (DH v'Chosav Rabeinu).