Rambam - 1 Chapter a Day

I.e., the seven days of mourning include the Sabbath; there is no need to observe an eighth day. The rationale is that since the private aspects of the laws of mourning are observed on the Sabbath, it is included in the reckoning of the seven days.

This is considered a private matter. For as reflected in the notes to Chapter 5, Halachah 19, even during the week, one was not required to veil one’s head in public.

I.e., washing one’s face, hands, and feet with water that was heated before the Sabbath. Among the private matters that are forbidden on the Sabbath is also Torah study. See Shulchan Aruch (Yoreh De’ah 400:1) for details.

And thus wear fresh clothes in honor of the Sabbath.

The Halachic authorities debate whether the intent is from Minchah Gedolah (from half an hour after noon onward) or from Minchah Katanah (from nine and a half seasonal hours after sunrise onward). See the Kuntres Acharon to ch. 251 in Shulchan Aruch HaRav which, on the basis of the Rambam’s ruling in Hilchot Tefilah 1:5, 3;2, states that, throughout the Mishneh Torah, whenever the term Minchah is mentioned without any further description, the intent is Minchah Katanah, i.e., the late afternoon.

And thus the seven days of mourning will conclude on Sunday mourning.

I.e., Pesach, Shavuos, and Sukkos.

Since the festivals are characterized by happiness and joy, any observance of the rites of mourning is inappropriate. As Mo’ed Kattan 14b states, the positive commandment (Deuteronomy 16:14): “And you shall rejoice in your festivals” takes precedence over the obligation to mourn, for the obligation to rejoice is incumbent on the Jewish people as a whole.
The Rambam’s wording implies that no mourning rites at all should be observed on the festivals, not even the private aspects of mourning that are observed on the Sabbath. The Tur and the Shulchan Aruch (Yoreh De’ah 399:1) rule that if a person did not observe the mourning rites at all before the festival, he should observe the private aspects of mourning during the festival.

I.e., here the intent of the word sha’ah is not an hour.

If a mourner observed the mourning rites for the briefest time before these holidays, the holiday forces him to stop that observance and he is not required to resume these rites.

The Radbaz explains that, according to the Rambam, even though Rosh HaShanah is followed by Yom Kippur and Yom Kippur is followed by Sukkos, since Rosh HaShanah and Yom Kippur are not festivals in the complete sense of the term, it is not appropriate that the person should have the entire mourning experience eliminated so drastically. The Kessef Mishneh explains that it is not appropriate that both dimensions of mourning be cut short for the same death.
The Hagahot Maimoniot, the Tur, and the Shulchan Aruch (Yoreh De’ah 399:9-10) differ and maintain that Yom Kippur and Sukkos do nullify all mourning rites. This is the universally accepted practice at present.

To complete the Sheloshim period of mourning described in Chapter 6.

And thus is considered as equivalent to seven days. Nevertheless, it is not considered as a festival in the sense that it has the power to nullify the Sheloshim mourning, because there was never any dimension of the Sheloshim mourning observed in a distinct manner (Turei Zahav 399:6).

In the diaspora, one need observe only eight days of mourning. Although mourning is not observed on Simchat Torah, it is also counted as one day in the Sheloshim reckoning [Shulchan Aruch (Yoreh De’ah 399:11)].

The Ramah (Yoreh De’ah 399:3) states that on the day before other festivals, one should perform these activities shortly before nightfall. On the day before Pesach, leniency is granted and the mourner should perform these activities shortly after midday.

The earlier part of the day is considered as the conclusion of the 30 day period of mourning.

See Chapter 6, Halachah 3.

Since this dimension of mourning is not limited to the 30 day period, it is not nullified by the festivals. Similar concepts apply with regard to the other special aspects of mourning associated with the death of one's parents mentioned in that chapter.

On the festival, he may wash (in cold water, or with hot water during Chol HaMoed) for none of the mourning rites are observed during a festival as stated in Halachah 3.
The Shulchan Aruch (Yoreh De’ah 399:5) states that with regard to laundering one’s clothes, one may launder them after midday, but refrain from wearing the laundered clothes until the onset of the festival. The Shulchan Aruch (loc. cit.) also mentions that there are opinions that allow one to wash shortly before the onset of the festival and the Ramah rules that it is customary to accept that view.

I.e., subtracting the days mentioned in Halachot 3 and 4.

The commentaries question why the Rambam mentions “the day of death” when he states previously that the 30 days of mourning are from the day of the burial.

When it is forbidden to cut one’s hair.

I.e., on Chol HaMoed, the intermediate days of the festival. Generally, this is forbidden, but leniency is granted in the present instance, because he was prevented from cutting his hair before the festival by forces beyond his control. See Hilchot Sh'vitat Yom Tov 7:17-18.

I.e., in situations when the seventh day of mourning falls on the day before any of these holidays and that day is the Sabbath.

For according to the Rambam, the laws of mourning should not be observed during the festival at all. The Rambam, nevertheless, rules that the expressions of grief and comfort associated with the burial should be observed during Chol HaMoed as stated in the following chapter. The Tur and the Shulchan Aruch (Yoreh De‘ah 399:2) differ with the Rambam and state that the private dimensions of the mourning laws must be observed during the festivals.

The Shulchan Aruch (loc. cit.) states that certain leniencies can be observed with regard to the performance of work. After seven days pass after the death of the deceased, other people can perform the mourner’s work in their own homes and the mourner’s servants may perform his work in a discreet manner in his home.

Making no further reductions. Even when a person dies in the midst of Sukkos, Shemini Atzeret does not cause the number of days to be reduced, because he did not (fully) observe any days of mourning [Shulchan Aruch (loc. cit.)].

I.e., when a person dies in the middle of a festival.

And including the last day of the holiday.

And according to Scriptural Law, one should observe the mourning laws on that day.

I.e., Pesach or Sukkot.

As mentioned in Hilchot Sh'vitat Yom Tov 1:23, "Everything necessary [for the burial] may be performed . . . . With regard to a corpse, the second day of a holiday is considered like an ordinary weekday. This applies even with regard to the second day of Rosh HaShanah." As mentioned in the notes to that halachah, in the present age, it is not customary to follow this leniency and burials are usually postponed until after the holiday.

See Chapter 1, Halachah 1. The Shulchan Aruch (Yoreh De’ah 399:13) emphasizes that this law only applies with regard to those individuals for whom we are required to mourn according to Scriptural Law.
The Shulchan Aruch (loc. cit.) continues that the present custom is not to mourn for any relative on the second day of a festival even if the person died and was buried on that day. The Ramah states that the ruling is based on the premise that there is no Scriptural obligation to mourn.

Hilchot Kiddush HaChodesh 5:8 explains that the two days of Rosh HaShanah are considered as a single continuum of holiness since even in the time when the new moon was sanctified through the testimony of witnesses, Rosh HaShanah was often observed for two days.