Gemara

17b - Mishnah: If Yom Tov is on Yom Rishon, we are Tovel everything before Shabbos;

Beis Hillel say, we are Tovel Kelim before Shabbos. People may be Tovel on Shabbos.

Question: All forbid Tevilas Kelim on Shabbos. What is the reason?

Answer #1 (Rabah): This is a decree lest one carry them four Amos in Reshus ha'Rabim.

Questions (Abaye): If one has a pit (Mikveh) in his Chatzer, why is it forbidden? Why is it forbidden on Yom Tov?

Answers (Rabah): We decree lest one be Tovel them in a pit in Reshus ha'Rabim. We decree on Yom Tov lest one be Tovel on Shabbos.

Question (Abaye): We do not make such decrees, e.g. to forbid Hashakah (touching water in a Keli to a Mikveh to Metaher the water) lest one be Tovel a Keli!

(Mishnah): All permit Hashakah in a stone Keli (which is not Mekabel Tum'ah), but we may not be Matbil (in a wooden Keli).

Answer (Rabah): Surely, one does Hashakah only if he has no other water. Such a person is careful with his water. (It is rare that it would become Tamei. Chachamim decree only in normal cases.)

Answer #2 (to Question (3) - Rav Yosef): It is a decree lest one squeeze (water out of clothing).

Question (Abaye): Why is it forbidden to be Tovel Kelim for which this is not a concern (e.g. a knife)?

Answer (Rav Yosef): It is a decree lest one be Tovel other Kelim and squeeze them.

The above questions are asked; the same answers are given.

Answer #3 (Rav Bivi): One may not be Tovel on Yom Tov a Keli that became Tamei before Yom Tov. This is a decree lest one delay their Tevilah.

A Beraisa supports Rav Bivi.

Answer #4 (Rava): It is forbidden because it looks like Tikun (fixing) Kelim.

Rishonim

The Rif brings the answers of Rav Yosef and Rav Bivi.

Ran (DH Gemara): We decree lest one delay Tevilas Kelim and use them b'Tum'ah. Also, it is improper to intentionally leave labors for Yom Tov.

Or Some'ach (Hilchos Yom Tov 4:17): The Rif omits Rabah's reason because Beis Hillel does not forbid Hotza'ah (of a child or Sefer Torah) on Yom Tov lest one do so on Shabbos.

Rambam (Hilchos Shabbos 23:8): One may not be Tovel Tamei Kelim on Shabbos because it looks like Tikun Keli.

Hagahos Maimoniyos (5): A Beraisa (18a) permits scheming to use a Keli to draw water in order to be Tovel it. Also, people may be Tovel because it looks like they intend to cool off. (Here also, it looks like he intends to draw water!)

Rambam (Hilchos Yom Tov 4:17): If a Keli became Tamei before Yom Tov, one may not be Tovel it on Yom Tov. This is a decree lest one leave it Tamei (until Yom Tov). If one needed to Metaher water inside the Keli, one may be Tovel the Keli with the water.

Magid Mishnah (17): The Rambam rules like Rav Bivi because a Beraisa supports him.

Lechem Mishneh (Shabbos 23:8): Regarding Shabbos the Rambam rules like Rava, but regarding Yom Tov he rules like Rav Bivi.

Chasam Sofer (YD Teshuvah 196): We are not concerned for mishap (due to delaying Tevilah) in less than 21 days, therefore Rab Bivi's reason applies to Yom Tov, but not to Shabbos. For the sake of Simchas Yom Tov, on Yom Tov we do not decree due to squeezing or Tikun Keli.

Rambam (18): If a Keli became Tamei on Yom Tov, one may be Tovel it on Yom Tov. If before Yom Tov a Keli became Tamei through a Tamei liquid, which is a Vlad ha'Tum'ah, one may be Tovel it on Yom Tov, because mid'Oraisa it is Tahor.

Magid Mishnah: The Rashba forbids Tevilah on Yom Tov of Kelim (for eating) bought from Nochrim, unless it is like Taharah of the Keli. I.e. one may draw water from a spring using a Keli suited for this, and this is Metaher it. The Rambam holds that Tevilah of Kelim (of Nochrim) is mid'Rabanan, so he would permit this in any case, just like a Keli that became Tamei mid'Rabanan. However, I agree with the Rashba. Even the opinion that is not concerned for Tikun says so only regarding Tum'ah, for a Tamei Keli can be used. But Klei Nochrim are totally useless before Tevilah, so all forbid due to Tikun.

Perush ha'Mishnayos (Beitzah 2:2): Tevilah of Tamei Kelim is Asur on Shabbos and Yom Tov because it looks like Tikun Keli.

Rosh (2:12): Why did the Rif discuss Tevilas Kelim? It does not apply nowadays! (The Rif and Rosh only bring Halachos relevant nowadays.) Also, according to the two reasons he gives, it should be permitted to be Tovel new Kelim (of Nochrim) on Yom Tov! Rather, the primary reason is lest one carry in Reshus ha'Rabim. This is why we decreed against Shofar, Lulav and Megilah on Shabbos. Also, the Halachah follows Rabah against Rav Yosef. We are also concerned for Rava's reason, for he is Basra. For both of these reasons we may not be Tovel new Kelim on Yom Tov. (One may carry food through Reshus ha'Rabim, but taking Kelim to be Tovel them is only Machshirim (things used to prepare food).)

Rebuttal (Taz OC 323:5): We cannot rely on the Kelal that the Halachah follows Rabah against Rav Yosef, because Rav Bivi also argues. Also, granted that we decree lest people carry on Shabbos, only Rabah forbids Yom Tov lest people carry on Shabbos. Rav Bivi holds that we do not make any decree! Also, it is not clear that Rava would forbid Tevilah of new Kelim. Since it is mid'Rabanan, perhaps it is permitted, like a Keli that became Tamei mid'Rabanan! The Magid Mishnah said that Tevilah of new Kelim could be more stringent than Tum'ah mid'Rabanan, but perhaps it is not. The Rif brings the answers of Rav Yosef and Rav Bivi. Both surely permit new Kelim. Also the Rambam seems to permit them. In Hilchos Shabbos he relies on what he wrote in Hilchos Yom Tov, that only Kelim that are Tamei mid'Oraisa are forbidden. This is unlike the Maharshal, who says that in Shabbos the Rambam wrote (Stam) Kelim to include new Kelim.

Poskim

Shulchan Aruch (OC 323:7): (On Shabbos) one may be Tovel Kelim bought from Nochrim that require Tevilah. Some forbid.

Beis Yosef (DH ul'Inyan): Since the Rif and Rambam permit, we allow this.

Rebuttal (Yam Shel Shlomo 2:19): The Rambam (Shabbos 23:8) forbids because it looks like Tikun Keli. The same applies to new Kelim of Nochrim! Even Rav Yosef forbids; once Chachamim decreed lest people squeeze garments, they forbade all Tevilas Kelim. Even Rav Bivi forbids, lest one use them before Tevilah. The Rif and Rambam bring Rav Bivi to teach that one may not delay Tevilah of new Kelim. We may not infer that the other reasons do not apply. The Rambam also brings Rava's reason to explain why Haza'as Mei Chatas on people is forbidden, but Tevilah is not.

Tosfos Yom Tov (2:2 DH v'Adam): We are not concerned lest people delay Tevilah of new Kelim, for they do not use them at all. (Only regarding Tamei Kelim, which may be used for Tamei food, we are concerned lest they be used for Taharos.) The Gemara brings Rava after the Beraisa supporting Rav Bivi to teach that the Beraisa does not show that we are not concerned for the reasons of the other Amora'im.

Mishnah Berurah (30,31,32): The latter opinion forbids even if he received it on Shabbos, and even if it is needed for Shabbos. It forbids even glass Kelim, even though all agree that their Tevilah is mid'Rabanan. The first opinion permits even if he had the Keli before Yom Tov. It seems that it permits even metal Kelim, even though some say that their Tevilah is mid'Oraisa.

Kaf ha'Chayim (64): Sha'agas Aryeh (56,57) permits Tevilah of glass Kelim, but not metal, during Bein ha'Shemashos before Shabbos and Yom Tov. Bein ha'Shemashos after Shabbos or Yom Tov is Asur, since it is for the sake of Chol.

Mishnah Berurah (33): The Darchei Moshe connotes that the primary opinion forbids. If one is in doubt whether or not a Keli requires Tevilah, he may rely on the first opinion if it is hard to do the other methods the Shulchan Aruch brings.

Shulchan Aruch (ibid.): One with Yir'as Shomayim will fulfill all opinions and give it to a Nochri for a gift and borrow it, then he may use it without Tevilah.

Question (Tosefes Shabbos, cited in Machatzis ha'Shekel on Magen Avraham 12): This does not fulfill all opinions! One may give a gift on Shabbos only for needs of Shabbos. According to the first opinion, one may be Tovel it, so there is no need (or Heter) to give it to the Nochri!

Answer (Machatzis ha'Shekel, ibid.): One may give a gift on Shabbos for the sake of any Mitzvah. One with Yir'as Shomayim wants to fulfill all opinions; this is like the needs of a Mitzvah.

Rema: If it is a Keli that holds water, one may fill it with water from a Mikveh, and this is Tevilah.

Mishnah Berurah (36): He may not bless, for then it would be clear that it is for Tikun. Since he loses the Berachah, he should do this only if he cannot use another Keli.

Kaf ha'Chayim (48): One may not give it to his slave, or to his Nochri servant.

Kaf ha'Chayim (50): After Shabbos he is Tovel it. Some say that he need not, so he does not bless. It is best to Tovel it with a Keli that requires a Berachah