Gemara

(Rav): Ner Shabbos is obligatory. Washing the hands and feet in hot water Arvis is Reshus (optional).

(Rava): I say that washing is a Mitzvah.

Question: What is the Mitzvah?

Answer: Rav Yehudah taught in the name of Rav that on Erev Shabbos they would bring to R. Yehudah a basin of hot water. He would wash his face, hands and feet.

Question: What does "Nashisi Tovah (I forgot what is good)" refer to?

Answer #1 (R. Yirmeyah): This is a bathhouse.

Answer #2 (R. Yochanan): This is washing hands and feet in hot water.

31a: On Erev Shabbos, Hillel was washing his hair. Ploni went by Hillel's door asking 'who here is Hillel'...

Sanhedrin 95a: On Erev Shabbos, Avishai ben Tzeruyah was shampooing his hair...

Beitzah 27b: A man came to ask Rava about a blemish in a Bechor on Erev Yom Tov, when Rava was shampooing his hair...

Nedarim 81a (Shmuel): Dirt that accumulates on an uncombed (some say - unwashed) head leads to blindness.

Rishonim

Rambam (Hilchos Shabbos 30:1): Oneg Shabbos and Kevod Shabbos are Mitzvos mid'Rabanan explicit in the Navi.

Rambam (2): There is a Mitzvah to wash the hands, feet and face on Erev Shabbos due to Kevod Shabbos.

Rosh (2:18): R. Tam says that Ner Shabbos is called a Chiyuv compared to washing hands, feet and face, which is not such a Mitzvah.

Mordechai (287): Avi ha'Ezri learns from Shabbos 25b that it is a Mitzvah to bathe on Erev Shabbos in hot water. It is also a Mitzvah to shampoo the hair, like we find regarding Hillel, Avishai and Rava.

Rashi (25b DH Rechitzas): Washing the hands and feet in hot water on Shabbos night is Reshus.

Note: The Rashba says that this refers to Erev Shabbos. It seems that most Meforshim explain like this.

Poskim

Shulchan Aruch (OC 260:1): On Erev Shabbos, there is a Mitzvah to wash (Rema - the entire body).

Gra (DH Kol): We learn that it is a Mitzvah to wash the entire body from the Amora'im's explanation of "Nashisi Tovah."

Machazik Berachah (of the Birkei Yosef, 1): Ra'avan says that there is a Mitzvah to heed Chachamim and wash the entire body on Erev Shabbos. Also Eliyahu Rabah says so in his name. Granted, the Gemara (Chulin 106a) said so about Netilas Yadayim. However, we do not find that Chachamim commanded about washing the entire body. We merely find that this was the custom of one Chasid, i.e. R. Yehudah. This was one of thousands of details and matters of Chasidus and meticulous Mitzvah observance that he did. Whenever the Gemara discusses a Stam Chasid, it was R. Yehudah (Stam, who is R. Yehudah bar Ilai) or R. Yehudah ben Bava. The Gemara did not explicitly say that it is a Mitzvah to heed Chachamim. Perhaps Ra'avan means that Rav Nachman taught that it is a Mitzvah of Kevod and Oneg Shabbos. He supported this from R. Yehudah's custom. Ra'avan teaches that this is not merely Chasidus. It is proper for everyone to do so. How did Rav Nachman derive that it is a Mitzvah? We learn about R. Yehudah's custom from Rav, and Rav said that it is Reshus! Even though Rav Nachman said 'I say...' he comes to explain Rav. Rav taught that Ner Shabbos is obligatory, therefore [for contrast] he called washing hands and feet Reshus, but really it is a Mitzvah. Rav did not need to explain this, for he relied on his teaching about R. Yehudah's custom. Also in Chulin (105a) we call a Mitzvah (Netilas Yadayim) a Chiyuv in contrast to Reshus. Alfasi Zuta explains like I said. The She'altos (Tetzaveh) cites Rav to say that washing the hands, feet and face is a Chiyuv. Either this was his text in the Gemara, or there a printing mistake in the She'altos.

Birkei Yosef (2): Eliyahu Rabah says that it is a bigger Mitzvah to wash the entire body. The Tur connotes like this. If so, why didn't R. Yehudah do so? Ra'avan says that he did so [washed only his hands, feet and face] when there was no bathhouse available. This is difficult. Also, Rav said that hands, feet and face are Reshus. Do not say that the entire body is a Mitzvah. If so, why did he distinguish between Ner Shabbos and washing? He should have distinguished within washing [between hands, feet and face, and the entire body]! Also, it seems that the episodes with Hillel, Avishai and Rava were not in the bathhouse. Was it impossible for all of them to bathe?! The Mordechai and Agudah mention a Mitzvah only regarding hands, feet and face. Surely the Tur means that the entire body is the ideal Mitzvah. It is a great honor to Shabbos. If one does not do so, there is no Aveirah or punishment. The Darchei Moshe brings so from Or Zaru'a regarding shampooing. Washing the hands, feet and face in hot water is different. One should not refrain from it. We can say that Hillel, Avishai and Rava used to bathe the entire body; the episodes happened to occur while they were shampooing. We can say that R. Yehudah used to immerse in a Mikveh or river, like it says in the Medrash of R. Shimon bar Yochai, and he washed his hands, feet and face in hot water. The ideal Mitzvah to bathe the entire body is for one who does not immerse. I say that the Tur learns from Shabbos 25b. R. Yirmeyah said that "Nashisi Tovah" is a bathhouse, and R. Yochanan said that it is washing hands and feet in hot water. R. Yirmeyah connotes that washing the entire body is a Mitzvah. R. Yochanan was not able to wash even the hands, feet and face in hot water. He admits that washing the entire body is a great[er] matter.

Aruch ha'Shulchan (2): R. Yehudah's head hurt him (Nedarim 49b). Such a person cannot enter a bathhouse, due to the heat. Therefore, he did not bathe his head.

Note: R. Yehudah said (there) that due to the four cups of wine on Pesach, he had such pain that he tied his temples until Shavu'os. Perhaps the rest of the year, he had a less severe headache from drinking wine (perhaps only part of the cup) of Kidush and Havdalah from the previous Shabbos.

Mishnah Berurah (3): The Shulchan Aruch refers to washing the entire body in hot water.

Taz (1): If he cannot bathe on Erev Shabbos, he should bathe as close to Shabbos as possible.

Bi'ur Halachah (DH Mitzvah): Even one whose sole occupation is Torah should take time off to bathe in hot water, for R. Yehudah did so, although it says so only regarding his hands, feet and face.

Shulchan Aruch (ibid.): (Rema - and if he cannot, he washes) the hands, feet and face in hot water on Erev Shabbos.

Birkei Yosef (1): The Rambam and R. Yerucham say that the Mitzvah is due to Kevod Shabbos. The Gemara connotes like Ra'avan that it is a Mitzvah to heed Chachamim. However, we can say that Rav Nachman teaches that Rav holds that it is a Mitzvah, due to Kevod Shabbos; he learned from R. Yehudah.

Mishnah Berurah (1): This is not an absolute Chiyuv. One who fulfills it is rewarded. One who does not fulfill it is not punished. One must be careful not to come to an Isur Shabbos, e.g. in winter when people finish close to dark. Even if he finishes bathing before Shabbos, sometimes one combs his hair at the end, which is a Melachah mid'Oraisa, or squeezes out water absorbed in the towel, which is laundering. Anyone who can protest against this must do so.

Mishnah Berurah (2): The Mitzvah is also for women. In winter, if they do not have time, they should wash at least the face and hands. Likewise, this is enough for a man if he lacks time.

Mishnah Berurah (4): Nowadays people are not careful about washing the feet. Perhaps they were careful only in their lands, where people walked barefoot, and they washed the dust and earth off the feet.

Mishnah Berurah (5): The same applies to Erev Yom Tov.

Kaf ha'Chayim (1): On Erev Shabbos, after cutting his nails, the Ari Zal would wash his face and then his hands in hot water, dry them, and then wash his feet in hot water. One must wash the right hand before the left, and the right foot before the left.

Kaf ha'Chayim (3): The Rambam (Hilchos De'os 4:16) says that it is healthy to bathe the body once every seven days in hot water that does not scald the body. One should do so on Erev Shabbos Lichvod Shabbos, and automatically this is a cure. Pesachim 111b says that one should not put on his shoes when his feet are still wet from bathing, for this blinds. "Hash-m guards the simple" (who do not know to be careful about such matters).

Kaf ha'Chayim (4): The Ari Zal says to immerse twice on Erev Shabbos, with special intents for certain names of Hash-m. Some Chasidim immerse 13 times.

Bi'ur Halachah (DH b'Chamin): One does not fulfill the Mitzvah with cold water. It is not clear whether lukewarm water suffices.

Shulchan Aruch (ibid.): It is a Mitzvah to shampoo the hair.

Bach (1): The Tur mentions only washing the hands, feet and face, but it seems that one must also shampoo the hair in hot water. This follows from a Kal va'Chomer, for dirt that accumulates on an unwashed head harms the eyes. If one shampoos on Thursday, this does not honor Shabbos, unless he cannot bathe on Erev Shabbos.

Bi'ur Halachah (DH Lachuf): The Bach mentions shampooing in hot water. The Poskim did not mention this.