Gemara

111b - Suggestion: One is liable for a camel-driver's knot, i.e. tying [the end of the reins] onto the ring in a camel's nose.

Rejection: This is not permanent!

One is exempt for this, but it is forbidden.

(Mishnah): Other knots are permitted. A woman may tie the straps of her cloak...

Question: This is obvious! (She unties it every day.)

Answer: The case is, there is one strap above and one below. It suffices to untie one to remove her cloak;

One might have thought that we are concerned lest she be Mevatel one (permanently leave it tied). The Mishnah teaches that this is not so.

One is exempt for tying shoes like Rabanan, but it is forbidden.

Shoemakers permanently tie the strap onto the sandal of merchants. One is liable for this;

Other people tie the strap on by themselves. One is exempt for this, but it is forbidden;

If two people use a sandal, it is permitted. (Each must retie it to fit his foot. It is untied every day.)

Rishonim

Rosh (15:1): A knot that lasts a week or more is Asur l'Chatchilah.

Mordechai (386): The Ri says that Rabanan may not tie their shoes, for they remove them only on Shabbos night. Similarly, it is proper to tie the belt on Shabbos with only a bow. However, the Yere'im permits. He says that Rabanan tie their shoes loosely, and they can remove them without untying, so sometimes they leave it tied permanently.

Poskim

Shulchan Aruch (OC 317:1): If one ties a permanent and professional knot, he is liable. If one tied a permanent, amateur knot, he is exempt.

Taz (1): Rashi and the Rosh do not distinguish between whether it is a strong professional knot. It depends only on the intent of the one who tied it. If he intended it to last forever, i.e. as long as possible, and he will not need to untie it, and he did not fix a time in his mind when to untie it, he is liable. If he fixed any time, he is exempt, but it is forbidden, for within this time it is called permanent. If he intends to untie it on the same day, this is not called any time at all, and it is permitted l'Chatchilah. The Tur holds like this. He mentions a knot destined to last seven days. Really, the same applies to any amount of time more than one day.

Rebuttal (Bi'ur Halachah DH ha'Kosher): If so, even the knot of a professional sandal-maker, camel-driver or ship-driver is not called a knot [and it is permitted] if he intends to untie it the same day! People normally make this permanently. It does not cease to be considered a knot due to intent of the one who tied it! The exemption of Rabanan's shoe knot, or one who ties his own sandal straps, is because it is normally tied temporarily. This is like the exemption for a sandal that people alternate using. (Each changes the knot to fit his foot before wearing it.) It is not called a knot, even if it is strong like a professional's knot. This is because they usually make a temporary knot. However, all makes a [standard] sandal knot be permanent! If one tied it strong, his intent to untie it the same day is not Mevatel it from being called a knot. Surely it is forbidden [at least] mid'Rabanan. The Kolbo and Yere'im forbid a temporary knot if people sometimes reconsider and leave it. Here, since all make it permanent, the Torah forbids it. This was clear to the Beis Meir. This answers the Pri Megadim's question why one cannot make Tzitzis on Shabbos, with intent to untie them on Motza'ei Shabbos.

Rema: Some say that any knot not normally opened on the same day is called permanent.

Beis Yosef (DH Chasuv): Shibolei ha'Leket (124) brings from the Tosefta (13:16) that exempts for a knot destined to last a week or a month. If he intends only for a day, it is permitted.

Beis Yosef (DH v'Chasav): Sefer ha'Terumah (243). Hagahos Maimoniyos (10:3) and the Mordechai explain that Rabanan remove their shoes only from Shabbos to Shabbos. Therefore, one may not tie a belt that will remain tied until next Shabbos. It seems that the Tur permits any knot destined to last less than seven days. He forbids "because they untie only when they change [the next Shabbos]." If they untied earlier, it would be permitted. However, perhaps he merely explained when they change, but really we forbid any knot destined to last more than a day. It seems that Maharam (434) holds like this.

Kaf ha'Chayim (14): The Acharonim say that this opinion is primary.

Mishnah Berurah (6): If it will be untied at night, on Motza'ei Shabbos, it is not called permanent, and it is permitted l'Chatchilah. However, one may tie on Shabbos night and untie it on Shabbos day, even though it is not on the same day, for anything within 24 hours is called the same day.

Minchas Yitzchak (8:19:2): One who ties the Sefer Torah at Shabbos Minchah should not make a knot and bow, for it will not be untied the same day [until Monday]. Rather, he makes just a knot and tucks the ends under it. If the Sefer won't be used until next Shabbos, even the next opinion in the Rema forbids.

Rema: Some are lenient to say that until seven days, it is not called permanent.

Beis Yosef (DH veha'Rosh): Rashi holds that a temporary knot is one that is untied every day. He and the Rosh are Mechayev for a knot meant to last many days, even if an amateur tied it. If it is meant to last a number of days, but not many days, e.g. a sandal [it seems that this should say shoe - Hagahos Tur ha'Shalem 8] of Rabanan, one is exempt, but it is forbidden. Also the Tur says so. It seems that he forbids anything made to last more than one day, for he permits only what is destined to be untied the same day. However, he also says that one is exempt for what is destined to last seven days, but it is forbidden. This implies he permits what is destined to last less than seven days. He did not mention seven days to obligate for what lasts more than seven days, for it is considered permanent. Rashi (112a DH Kitra) explained that one may not tie [the end of the reins] onto the ring in a camel's nose, for sometimes one leaves it there a week or two. Amateurs may not tie sandal straps, for sometimes one leaves it there a week or a month (DH bid'Chumreta). This shows that one is exempt even for something that can last two weeks or a month. Rather, whatever is not destined to last seven days is called destined to be untied every day, and it is permitted. The Tur learned from Rashi. In both cases, Rashi said that sometimes it lasts a week. This implies that if it will last less than this, it is permitted. The Mordechai connotes like this.

Beis Yosef (DH veha'Gaon): Mahari Avuhav brings from R. Peretz that a knot destined to last eight days is called permanent. Perhaps the Tur teaches that one is exempt for a knot destined to last seven days, for one is liable for more than this. If so, perhaps he permits only what is destined to be untied every day. Mahari Avuhav said that since the Tur brought Sefer ha'Terumah's law of the belt, this connotes that less than seven days is permitted. One can reject this, like I wrote above.

Beis Yosef (DH v'Rabbeinu): R. Yerucham says that a knot destined to last half a year or a year is permanent, and one is liable for it. A knot destined to last three days or a week or two is Asur l'Chatchilah. He understands that Rashi did not mention a week to permit less than this, rather, to teach that even if it will last a week or longer, he is exempt. Even less than a week is forbidden. However, a knot destined to last less than three days is considered destined to be untied every day, and it is permitted.

Magen Avraham (2): It is permitted l'Chatchilah.

Kaf ha'Chayim (15): The Rema discusses up to but not including seven days. The Magen Avraham says that this opinion permits all knots destined to last less than seven days. The Taz forbids but exempts for any knot destined to last more than one day [but not permanently]. Eliyahu Rabah says that there is no necessity to say so, but he says that the primary opinion forbids anything destined to last more than one day.

Shulchan Aruch: A temporary knot that is not professional is permitted l'Chatchilah.

Bi'ur Halachah (DH she'Eino): These are the Rambam's words. It is even if it is made for a period of time. The Rosh permits only if it is not destined to last at all.

Shulchan Aruch (ibid.): For the need of a Mitzvah one may tie any temporary knot.

Question (R. Akiva Eiger): If a string of a Levi's harp broke, some Tana'im forbid tying it (Eruvin 103a). This is for a Mitzvah. We should permit tying it with intent to untie it the same day!

Answer (Bi'ur Halachah DH ha'Kosher): I answer like I said above. Most people make such knots permanently, therefore it is a Torah Isur.