Gemara

23b (Mishnah): Shabbos is Oleh (counts towards the days of Avelus) but does not cancel Aveilus.

Benei Galil and Benei Yehudah argued about whether or not Aveilus applies on Shabbos.

One says that Aveilus applies, for Shabbos is Oleh;

The other says that it does not apply, for the Mishnah teaches that Shabbos does not cancel. If Aveilus applied, there would be no need to teach that it does not cancel!

It says that Shabbos is Oleh for parallel structure with the Seifa, which says that the Regel is not Oleh (this will be explained).

The first opinion says that the Mishnah teaches that Shabbos does not cancel Aveilus (even though this is obvious) for parallel structure with the Seifa, which says that the Regel cancels.

Suggestion: Tana'im argue about this:

(Beraisa): If one's Mes is in front of him, on Shabbos he reclines and eats meat and wine. He blesses before and after eating, he joins a Zimun, and he is obligated in all Mitzvos;

R. Gamliel says, because he is obligated in these, he is obligated in all Mitzvos.

(R. Yochanan): R. Gamliel and Chachamim argue about marital relations.

Suggestion: Chachamim hold that Aveilus applies on Shabbos, and R. Gamliel disagrees.

Rejection #1: All hold that Aveilus does not apply on Shabbos. Chachamim exempt an Onen from relations because the Mes is in front of him.

Rejection #2: All hold that Aveilus applies on Shabbos. R. Gamliel obligates an Onen because Aveilus did not start yet.

Question (R. Yochanan): Does Aveilus apply on Shabbos?

Answer (Shmuel): It does not apply.

(Shmuel): On Shabbos, an Avel must fulfill 'Pachaz', i.e. (an acronym for) uncovering his head, turning his garment so the tear will be in back, and erecting his bed (to avoid public Aveilus). 'Natar', i.e. wearing shoes, relations, and washing his hands and feet in hot water at night, are optional.

(Rav): Also uncovering his head is optional.

Question: Surely, Shmuel says that wearing shoes is optional because not everyone wears shoes (so it is not public Aveilus). The same should apply to uncovering the head, for not everyone uncovers it!

Answer: This is like Shmuel taught elsewhere, that an Avel must cover his head like Yishmaelim (and no one else does so, so it is a clear sign of Aveilus).

R. Yochanan: This is only if he is not wearing shoes. If he is wearing shoes, it does not look like public Aveilus.

Rava: An Avel may go in his house wearing an Unkli (this will be explained).

Abaye saw Rav Yosef (during his Aveilus) with his head covered on Shabbos.

Abaye: Don't you hold that Aveilus does not apply on Shabbos?

Rav Yosef: R. Yochanan taught that private matters apply.

Kesuvos 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...

All 14 days he sleeps among men, and she sleeps among women.

4a: This supports R. Yochanan, who says that even though we do not show signs of Aveilus during the Mo'ed, private matters (relations) are forbidden.

Rishonim

Tosfos (23b DH Man d'Omar): By saying 'Shabbos is Oleh' without saying 'even though there is no Aveilus on Shabbos', this connotes there is Aveilus on Shabbos. The latter opinion rejects this. Aveilus does not apply on Shabbos or Yom Tov. Yom Tov is not Oleh because it is a time of Simchah; this does not apply to Shabbos. For parallel structure, the Mishnah said 'Shabbos is Oleh' without adding 'even though there is no Aveilus on Shabbos'.

Rif and Rosh (3:28): Aveilus does not apply on Shabbos. On Shabbos, an Avel must fulfill 'Pachaz' and 'Natar'. If he is wearing shoes, he need not uncover his head. We conclude that private matters, such as covering his head, washing in hot water, relations and similar matters apply in private.

Rosh (3:28): Nowadays people do not go barefoot, so he must wear shoes on Shabbos.

Rambam (Hilchos Evel 10:1): Aveilus on Shabbos applies only to private matters, such as covering his head, relations and washing in hot water. One may not show open signs of Aveilus. He wears shoes, erects his bed and gives Shalom to people. If he has another garment, he wears it. If not, he turns back the tear.

Beis Yosef (YD 400 DH v'Nir'eh): It seems that the Rambam obligates private matters such as covering the head apply only in private, like the case of Rav Yosef. However, if so we should likewise forbid wearing shoes in private! Rather, it seems that these signs of Aveilus apply even in public. They are called private matters because his shoes show that he is not (totally) observing Aveilus. Perhaps the Rambam rules like Rav, who says that even uncovering the head is optional. If so, one must do like he does during the week, since it does not look like Aveilus. The Gemara connotes that Rav says that it is optional because he does not require an Avel to totally cover the head, unlike Shmuel. The Rambam requires an Avel to totally cover the head. Perhaps even this is like Rav. Rav holds that it is optional on Shabbos because some people do so even during the week.

Rosh (ibid.): Learning Torah is a private matter. Since it is obligatory to review the Parashah (Shnayim Mikra v'Echad Targum) with the Tzibur, this is permitted, like Kri'as Shma. If he was called to the Torah he must read, for otherwise it is public Aveilus. R. Tam always used to be called third. When he was an Avel the Gabai did not call him, and he went up by himself, for if he did not it would be open Aveilus. The Yerushalmi says that greeting an Avel with Shalom on Shabbos depends on the custom. Relations are forbidden even during the Mo'ed. We learn from Kesuvos 4a; the seven days of Mishteh are like Mo'ed.

Poskim

Shulchan Aruch (YD 400:1): Shabbos does not interrupt Aveilus. It counts towards the seven days, because some laws of Aveilus apply, i.e. private matters, i.e. relations and washing. Public matters do not, so he uncovers his head, wears shoes, erects his bed, and changes garments or turns back the tear.

Gra (2): The Rif and Poskim rule like Shmuel because Rav Nachman holds like him, and also R. Yochanan, unlike Tosfos' understanding.

Beis Yosef (DH u'Mah she'Chosav Hilkach): The Mordechai says that removing shoes in the house is not a totally private matter, for people see this when they come to console him on Shabbos. It is not a totally open matter, for some people do not wear shoes for comfort or due to pain. Therefore, it is optional.

Shach (3): Nowadays we are not particular to turn the tear back, because we wear shoes.

Ramban (brought in Beis Yosef DH u'Mah she'Chosav Rabeinu): R. Chananel says that Unkli is a turban. Rashi says that it is a torn garment. This seems correct; when people visit him, he puts an intact garment on top of it. R. Yochanan said 'This is only if he is not wearing shoes.' The Rif says that this refers to covering the head, but one must turn back the tear in any case. Torn clothing is not called private. Even during the week it is not a decree of Shivah. (Except for Aveilus for a parent,) one may switch to an intact garment or turn the tear back. A Beraisa teaches that on Shabbos the tear must be in back. Teshuvas ha'Ge'onim disagrees. It says that even Pachaz is obligatory in public; in private, everything applies. The primary opinion forbids truly private matters, i.e. relations, bathing and anointing. Uncovering the head is optional.

Rema: He must uncover the head only if it is covered like Yishmaelim. The partial covering done in many places may be left on on Shabbos, since he wears shoes.

Rebuttal (Shach 2): Wearing shoes permits even covering the head totally! Mahariyo says that we forbid on Shabbos only Aveilus particular to the seven days. Since our custom is to cover the head even after Shivah, it is permitted on Shabbos. What is done only during Shivah is forbidden on Shabbos.

Rebuttal (of Mahariyo - Gra 399:4): We permit on Shabbos passive observances of Aveilus (Isurim), for this is not overt. What requires action is forbidden.

Shulchan Aruch (ibid.): Learning Torah is a private matter. Since it is obligatory to review the Parashah with the Tzibur, this is permitted, like Kri'as Shma.

Beis Yosef (DH v'Chosav ha'Mordechai): The Mordechai says that some consider learning Torah a private matter and forbid it. The Ri permits, for Torah gladdens the heart and he must gladden himself on Shabbos. We follow the majority, who forbid.

Taz (1): The Agudah forbids reviewing the Parashah. The Maharshal forbids during the week but permits on Shabbos because this is the time; it is an obligation of the day.

Shulchan Aruch (ibid.): If he was called to the Torah he must read, for otherwise it is public Aveilus. R. Tam always used to be called third. When he was an Avel the Gabai did not call him, and he went up by himself, for if he did not it would be open Aveilus.

Rema: Similarly, if the only Kohen in the Beis ha'Keneses is an Avel he should be called to read. Otherwise it is forbidden to call the Avel to read.