Gemara

(Beraisa - Rebbi): When we learned from R. Shimon, we would bring to him (on Shabbos) oil and a towel, transferring them from Chatzer to roof, from roof to Karfef (an enclosed place without a roof), and from Karfef to Karfef, until we reached the bathing spring.

Shabbos 48a: A slave in the Reish Galusa's house spread a turban over a flask and put a ladle on top. Rabah rebuked him. He explained to R. Zeira that he will see why he protested.

The slave later squeezed out water absorbed in the turban.

Question (R. Zeira): Since people may come to squeeze, why do Chachamim permit spreading a cloth over a flask?

Answer (Rabah): We are not concerned lest one squeeze a cloth, for people do not care if it is wet. People do not want a turban to be wet.

113b (Rava): One may not walk through a stream, lest his garments get soaked and he will come to squeeze out water.

146b (Mishnah): If one's clothes became soaked in water on the road, he may continue, this is no problem. When he reaches the outer gate (of the entrance to the city), he spreads them out to dry in the sun, but not in front of people.

(Rav Yehudah citing Rav): Anything forbidden due to Mar'is ha'Ayin (suspicion) is forbidden even in private.

147a (Mishnah): If one bathed in a cave or in Chamei Tiverya and wiped himself, even if he used 10 towels, he may not take them (with him).

However, even 10 people may use the same towel to wipe their hands, feet and face, and take the towel.

147b: The Reisha teaches that even though each towel is barely wet, since only one person wiped himself, he may not take them back lest he (forget, and) squeeze them;

The Seifa teaches that even though the towel is very wet, since there are many people, they may take it back. They will remind each other not to squeeze it.

(Beraisa): One may wipe himself with a towel and leave it in the window. He may not give it to a bathhouse attendant, for they are suspected of this matter (squeezing them, to give to another bather).

R. Shimon says, one may wipe himself with one towel and take it back home.

Question (Abaye): What is the Halachah?

Answer (Rav Yosef): R. Shimon permits (here), and also Rebbi, Shmuel, and R. Yochanan:

(Beraisa - Rebbi): When we learned from R. Shimon, we would bring to him oil and a towel...

(Shmuel): One may wipe himself with a towel and take it back home.

(R. Chiya bar Aba citing R. Yochanan): One may wipe himself with a towel and take it back home.

Question: R. Yochanan said that the Halachah follows a Stam (anonymous) Mishnah, Our Mishnah forbids even if he used 10 towels!

Answer: His text says 'these are the words of Ben Chachinai' (it is not a Stam Mishnah).

Rishonim

Rif and Rosh (Shabbos 62b and 22:12): R. Yochanan does not decree lest one squeeze a towel.

Ran (DH v'Ha): Why may one dry himself? We should be concerned lest he squeeze, just like we forbid spreading a turban over a barrel and walking through water! I answer that since everyone who bathes dries himself, if you forbid drying, you forbid bathing, and people cannot abide by this, like we say on 40a.

Rambam (Hilchos Shabbos 22:20): One who bathed in water may dry himself with a towel and bring it. We are not concerned lest one squeeze. He may not spread it (to dry), even in his house. This is a decree, lest one who sees say that he laundered it on Shabbos and spread it to dry.

Rashi (147b DH Ad): The Beraisa proves that one may take back the towel after drying with it, for presumably they did not leave the towel in a Hefker place.

Poskim

Shulchan Aruch (OC 301:45): If one's garments became soaked in water, he may walk wearing them. We are not concerned lest he come to squeeze them. He may not spread them to dry them, lest people suspect that he laundered them on Shabbos. It is forbidden even in an inner room, where no one will see. Chachamim forbade spreading them on Shabbos. If he spread from Erev Shabbos, he need not remove them.

Beis Yosef (DH Kasav): The Rashba says that one may put laundered garments on the roof to dry before Shabbos, even according to the opinion that rules like Rav Yehudah (who forbids due to Mar'is Ayin even in inner rooms). In Beitzah (9a), we say that Beis Shamai and Beis Hillel argue about moving a ladder like the Tana'im who argue about Mar'is Ayin. All agree that if one moved a ladder before Shabbos, he need not remove it before Shabbos lest people say that he moved it now (on Shabbos) to plaster his roof. Likewise, the concern lest people say that he laundered on Shabbos is only when he spreads clothes to dry on Shabbos.

Mishnah Berurah (167): The concern is only when he spreads clothes to dry on Shabbos, lest people say that had he laundered them from before Shabbos, he would have spread them before Shabbos. They do not know that they became soaked.

Kaf ha'Chayim (254): Rashi (146b) and Tosfos say that his garments fell in water on Shabbos. I.e. even if they became wet before he wore them, he may go in them, and all the more so if he was walking and they became wet in the rain. The Bach and Eshel Avraham hold like this. On Daf 65a, Rashi said that they became wet in the rain. This connotes if he was not wearing them when they became wet, he may not put them on. The Graz and Chayei Adam hold like this. It seems that this is because Tosfos (Beitzah 35b DH Mi) defended Rashi on 65a.

Kaf ha'Chayim (255): The Levush says that one is not so prone to squeeze the clothes he is wearing. Tosfos Yom Tov says that Chachamim did not want to forbid what one is wearing due to a decree lest one squeeze.

Magen Avraham (55): If they absorbed only a little water, one may spread them to dry. There is no concern lest people say that he laundered them. Some permit putting a little water on a garment! However, Sa'if 47 forbids even if they are wet from sweat.

Kaf ha'Chayim (257): Also Eliyahu Rabah forbids even if they are slightly wet.

Kaf ha'Chayim (258): One may spread diapers to dry in the house, or even in the sun in the Chatzer. Since there is excrement on them, it is clear that he did not launder them. Perhaps it is permitted even without excrement, unless it is totally soaked, for people know that infants urinate in them. Chayei Adam said that this requires investigation. Ben Ish Chai defends the custom to be lenient; one who is stringent will be blessed.

Kaf ha'Chayim (259): One may spread to dry hand towels that became wet from much usage, if some filth is seen in them. The same applies to handkerchiefs. They are like diapers.

Kaf ha'Chayim (260): If one transgressed and spread clothing to dry on Shabbos, he need not remove it. The decree was not to spread it on Shabbos. He already transgressed. One need not remove what is already spread from Erev Shabbos; this is no different.

Shulchan Aruch (46): If garments were soaked in water, one may not dry them near a fire.

Kaf ha'Chayim (267): The same applies to a tablecloth that became soaked.

Magen Avraham (57): We forbid only if they can get to Yad Soledes Bo, for then cooking and Libun (laundering or bleaching) applies. If not, we would forbid even in the sun!

Mishnah Berurah (170): In any case, he may not leave them the way people leave things to dry. This is always forbidden (even not near a fire).

Kaf ha'Chayim (265): Also when one is wearing the clothing, he may stand near a fire only if they cannot get to Yad Soledes Bo.

Kaf ha'Chayim (266): Eliyahu Rabah says that if one stood near a fire to get warm, he does not intend to dry them. However it is a Pesik Reishei. This requires investigation. Yafeh l'Lev permits on a cold day when it is normal to stand near a fire or in the sun. One may scheme and say that he wants to get warm.

Rema: One may not move them, lest he squeeze them. This is if he is concerned for the water.

Magen Avraham (58): He cites the Mordechai, who rules like the Mishnah. We rule unlike the Mishnah! We must say like the Ran, that we permit only what is needed for drying from bathing, for people cannot manage without this. It seems that 10 people may move it. This part of the Mishnah was not rejected.

Kaf ha'Chayim (268): Also the Beis Yosef permits this. Ben Ish Chai says that one may rely on this if a garment fell into the Mikveh and it will get ruined if one leaves it in until Motza'ei Shabbos.

Magen Avraham (58): Nowadays that people need not bathe (every day), drying should be forbidden. However, we can say that since Chachamim never forbade it, it is permitted. In any case, it is good to dry on something for which he does not care if it is wet.

Mishnah Berurah (173): The Gra connotes that people are not particular about a Stam towel.

Mishnah Berurah (171): This is only if they became soaked in much water. If they were soaked in only a little water, we are not concerned lest he come to squeeze them.

Mishnah Berurah (172): 'He is concerned for the water' means that he does not want them to be wet. There is no concern for rags that are always soaked; one may move them.

Kaf ha'Chayim (270): We do not forbid a garment soaked with red wine or other liquids that do not launder. L'Chatchilah, one may soak a garment in such liquids, e.g. to strain through it.

Rema: One may not walk on Shabbos in a place where he may slip and fall in water, lest his clothes get soaked and he come to squeeze them.

Kaf ha'Chayim (271): If so, it is permitted for a naked person. (Note: the same should apply to one who is wearing synthetic garments that do not absorb - PF.) However the Rif explains that we are concerned lest he drown.

Shulchan Aruch (48): One may dry himself with a towel and bring it in his hand. We are not concerned lest he squeeze it. One should not give it to bathhouse attendants, for they are suspected of squeezing.

Mishnah Berurah (174): One may dry even his entire body after bathing in cold water.

Mishnah Berurah (175): He may bring it home where there is an Eruv. Even though the Rema forbids moving something soaked, here is different. Since Chachamim permitted drying without concern for squeezing, since one cannot bathe without drying, they also permitted bringing the towel home. If so, after one brought it home and put it in its place, he may not move it. However, Eliyahu Rabah says that drying with a towel is considered a small amount of water, and there is no decree lest one squeeze. The Gra connotes like this.