Gemara

Mishnah: It is forbidden to cut hair or launder in the week in which Tish'ah b'Av falls.

Rav Nachman (and R. Elazar): It is forbidden to launder to wear, but one may launder and leave the clothing (for after Tish'ah b'Av);

Rav Sheshes: It is forbidden even to launder and leave.

Support (Rav Sheshes, for himself): The launderers of Rav's house are idle this week.

Question (Rav Hamnuna - Mishnah): On Thursday it is permitted (to launder) for Kavod Shabbos.

If this permits laundering to wear immediately, this does not honor Shabbos!

Rather, it permits laundering to leave (for after Tish'ah b'Av). This is permitted only on Thursday, but the rest of the week is forbidden!

Answer: Really, it permits laundering to wear immediately. The Mishnah discusses one who has only one garment;

Rav Asi: One who has only one garment may launder it on Chol ha'Mo'ed.

Question (Beraisa): It is forbidden to launder, even to leave for after Tish'ah b'Av. (In Bavel) our Gihutz (this will be explained) is like their laundering (in Eretz Yisrael);

We are not concerned for Gihutz of linen garments.

Rav Nachman and R. Elazar are refuted.

R. Yochanan: Even though we are not concerned for Gihutz of linen garments, one may not wear them in the week of Tish'ah b'Av.

Rishonim

Rif: The Halachah follows Rav Sheshes, who forbids even to launder and leave.

Ran (DH Garsinan and DH Hilkach): It says that our Gihutz is like their laundering. This implies that our laundering is permitted. if not, it should have said simply 'our Gihutz is forbidden'. Surely, the Heter for Gihutz of linen garments is if they are old. If they are new, Gihutz is forbidden, just like regarding Avelus. This implies that Gihutz of wool garments is forbidden even if they are old. Some say that Gihutz of linen garments is permitted because they do not get very clean. Therefore, for linen garments we permit Gihutz of Bavel and laundering of Eretz Yisrael. Therefore, one may give them to a launderer in the week of Tish'ah b'Av to wear them after the fast. However, R. Yehudah b'Ribi Reuven says that the essence of Gihutz is not laundering. Rather, it is pressing them, which makes them like new garments, which are forbidden whether they are white or colored. It is permitted for linen garments, for it does not make them like new. In Eretz Yisrael Gihutz does not make them like new. Laundering whitens them, so it is forbidden. Gihutz of new linen garments is forbidden everywhere. Laundering is permitted in Bavel because it is not a hilly land so the water (flows slowly and) is murky. Perhaps our lands are like Eretz Yisrael, and we may not launder linen garments in the week of Tish'ah b'Av, even to leave them. The Rambam seems to agree.

Ran (DH v'Chivus): One may not even spread laundered sheets on the bed or use laundered hand towels or tablecloths in the week of Tish'ah b'Av. The launderers of Rav's house were totally idle this week.

Rif and Rosh (4:32): Even though we are not concerned for Gihutz of linen garments, one may not wear them in the week of Tish'ah b'Av.

Rosh (4:32): Gihutz of linen garments is permitted because they are next to the skin and become dirty from sweat. The Yerushalmi says that when Tish'ah b'Av is on Shabbos, both weeks (before it) are permitted. Since the fast is postponed to the 10th, there is no week in which Tish'ah b'Av falls.

Rambam (Hilchos Ta'aniyos 5:6): In the week in which Tish'ah b'Av falls it is forbidden to launder and to wear Meguhatz clothing, even linen, until after the fast. Even to launder and leave is forbidden.

Magid Mishnah: The Ramban permits our laundering even for wool garments. The Rambam does not.

Lechem Mishneh: The Rosh asked, according to Rav Nachman the Mishnah should just forbid wearing laundered clothing. The Rambam answers this. It is forbidden to wear Meguhatz clothing during this week, but laundered clothing is permitted. Rav Sheshes agrees with this. This is unlike the Magid Mishnah, who says that the Rambam forbids wearing even laundered clothing.

Poskim

Shulchan Aruch (551:3): It is forbidden to launder in the week in which Tish'ah b'Av falls, even to leave the clothing for after Tish'ah b'Av. Even if he has only one cloak it is forbidden. What was laundered beforehand is forbidden to wear, spread on the bed or use for hand towels or tablecloths. Our laundering is permitted, but our Gihutz (passing a flat stone over a garment to smoothen it) is forbidden. We are not concerned for Gihutz of linen garments; it is like our laundering, which is permitted. This is only to do Gihutz for after the Tish'ah b'Av; one may not wear it in this week. The custom is to forbid even linen garments, and even our laundering, even for after the fast. One should not be lenient, since this is the custom. Further, perhaps our laundering is like that of Eretz Yisrael, and letter of the law forbids it. Some say that Gihutz is water with ashes or soap, and laundering is with water alone. If so, all our laundering is Gihutz, and letter of the law forbids laundering linen garments to wear them.

Beis Yosef (DH u'Mah she'Chosav v'Chivus): The Kol Bo says that our laundering is permitted, even to wear immediately. The Ramban and Tur forbid wearing it.

Beis Yosef (DH u'Mah she'Chosav Rabeinu): The Ramban says that we are not concerned for Gihutz of linen garments because it does not remove the sweat and dirt.

Kaf ha'Chayim (53): Even the Ramban says this only regarding garments worn next to the skin. He agrees that Gihutz applies to outer garments.

Beis Yosef (DH v'Ha): The Rambam did not permit laundering linen garments because the custom is to be stringent.

Beis Yosef (DH umid'Amrinan): The Terumas ha'Deshen says that the Maharam forbade laundering children's clothing. No one follows this.

Beis Yosef (DH Kosav ha'Ramban): The Ramban permits our laundering, for it is Meleches Arai. The same applies to Gihutz of linen garments, even in Eretz Yisrael. Nothing laundered may be worn in the week.

Beis Yosef (DH Kosav Avi): Avi ha'Ezri, Tosfos, the Mordechai, Rashi and the Rambam (according to the Magid Mishnah) say that it is our custom to forbid our laundering.

Rema: Our custom is to forbid all this from the beginning of Av until after the fast, if not for a Mitzvah. A woman who must wear (clean) underwear while counting seven clean days may launder underwear and a sheet to wear and spread under her in this week, but not on Tish'ah b'Av itself. Then, she just wears only a checked robe.

Kaf ha'Chayim (63): It is ludicrous to delay the seven clean days in order to be stringent about this.

Rema (ibid.): Also, for Kavod Shabbos we wear linen garments and spread Levenim like on other Shabbosos.

Taz (4): The Maharshal says that our custom is to forbid from Rosh Chodesh everything forbidden in the week of Tish'ah b'Av, except for what pertains to Kavod Shabbos, such as a shirt and towels. It seems that the custom is to be stringent about sheets.

Mishnah Berurah (29): One who has only one cloak may launder it from Rosh Chodesh until the week of Tish'ah b'Av.

Mishnah Berurah (32): One may launder on Thursday for Kavod Shabbos if he does not have a (clean) cloak. Certainly it is permitted through a Nochri.

Mishnah Berurah (33): The Rema permits changing tablecloths, but not changing sheets.

Kaf ha'Chayim (64): 'Like on other Shabbosos' suggests that everything is permitted. If so, why does the Rema specify linen garments? Perhaps the Rema permits everything before the Shabbos before Tish'ah b'Av, e.g. if Rosh Chodesh Av is Shabbos.

Mishnah Berurah (34): Poskim argue about whether or not after Rosh Chodesh one may give clothing to a Nochri on condition to launder it after Tish'ah b'Av. One may be lenient about linen.