Gemara

(Mishnah): One is liable for knots of camel-drivers and sailors.

Just like one is liable for tying them, he is liable for untying them.

R. Meir exempts for any knot that one can untie with one hand.

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.

Other knots are permitted. A woman may tie the straps of her cloak...

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

Others tie the strap on by themselves (it is not permanent, but it can be left for a while). One is exempt for this, but it is forbidden;

74b (Mishnah): Sewing two stitches [is an Av Melachah].

Question: Two stitches will come apart!

Answer (Rabah bar bar Chanah): He is liable only if he tied them.

157a (Mishnah): One may measure a rag or Mikveh;

A case occurred in which they tied a jug with a reed to determine whether or not there was a Tefach in a basket. This shows that one may measure and tie on Shabbos.

Rishonim

Rif (41b): A permanent knot that is not professional is Asur l'Chatchilah. A temporary knot is permitted.

Rambam (Hilchos Shabbos 10:1): A temporary knot that is not professional is permitted l'Chatchilah.

Rambam (2): Anything that an amateur ties to be permanent, he is exempt, but it is forbidden. Any temporary knot tied professionally is forbidden.

Rambam (4): One may tie a knot with anything proper for animal food.

Kaf ha'Chayim (317:8): This is because one cannot make a permanent knot with it. This applies only to things such as moist reeds, for when they dry up, they snap. It is forbidden with straw, Lulav leaves, or similar things that do not snap when they dry.

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.

Beis Yosef (DH v'Rabbeinu): R. Yerucham wrote like the Rosh, who did not stipulate that a professional tied it.

Bi'ur Halachah (DH ha'Kosher): A temporary knot for which is one is exempt is one not destined to remain forever (i.e. it is normally untied). This is even if it is made strongly, and one cannot untie it with one hand. The Rif, Rambam and Rosh agree about this. A proof is from the Tosefta (13:16), which exempts for any permanent knot that one can untie with one hand, or for a temporary knot that one cannot untie with one hand. (The Reisha is like R. Meir.)

Kaf ha'Chayim (2): Even though nowadays we do not bring Korbanos [or execute], the Mechaber taught for which knots one is liable, to teach about disqualifying a witness mid'Oraisa. If Ploni tied a knot for which one is liable, if he witnessed Kidushin [with only one other witness], she does not need a Get. If Ploni tied a forbidden knot for which one is exempt, he is disqualified only mid'Rabanan. If he witnessed Kidushin, she needs a Get. Also, we must announce about a witnesses disqualified mid'Rabanan. Also, we are lenient about a Safek about a knot for which one is exempt. Olas Shabbos says so. Also, the Teshuvah for a Torah Isur is different.

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

Kaf ha'Chayim (12): This opinion permits a double knot destined to be untied the same day, even though it is professional. The Rif and Rambam forbid. All permit a knot with a bow destined to be untied the same day. A bow without any knot is permitted even if it is for a long time.

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

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

Rema: The same applies to untying it.

Mishnah Berurah (7): Any knot that one may untie, if he is unable to untie it, he may cut it if needed. One may not do so in front of an Am ha'Aretz, lest he be lenient about other matters.

Shulchan Aruch: E.g. if a strap or rope broke and one tied it, he is exempt, for these are amateur knots. Any temporary knot tied professionally is forbidden.

Gra (DH v'Chol): The Beis Yosef brings that the Rif connotes like this. We learn from the sandal straps "that they (amateurs) tie." This is clear also from R. Yehudah (113b), who says "one is not liable for any knot that is not permanent." Surely he discusses a professional knot!

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

Beis Yosef (DH u'Mah): Rashi explains that we may tie a temporary knot l'Chatchilah for the sake of a Mitzvah, for its Isur is only mid'Rabanan.

Magen Avraham (3): Even a professional knot is permitted. If not, it is permitted even not for a Mitzvah. Why did they need a professional knot to measure? We must say that an amateur knot would not have sufficed.

Mishnah Berurah (11): I.e. one ties two ropes together in order to measure a Mikveh.

Rema: Some forbid untying any double knot, for we are not experts about what is called a professional knot, which one may not tie or untie even if it is temporary. This is the custom.

Beis Yosef (DH ul'Da'as): The Rif and Rambam exempt for a temporary knot of a professional, but it is forbidden.

Magen Avraham (4): The Rif connotes that it is a very tight knot.

Kaf ha'Chayim (22, citing Levushei Serad): If it is not tight at all, one may untie it. We are not experts about a knot that is a little tight.

Magen Avraham (5): This is like the Rambam. The Rosh and Shiltei ha'Giborim permit. The Gemara mentioned a professional knot, for normally they are permanent. This is unlike Olas Shabbos.

Machatzis ha'Shekel: I.e. the Rambam forbids tying and untying a double knot. The Rosh and Shiltei ha'Giborim permit tying and untying it.

Gra (DH v'Yesh Omrim): This opinion in the Rema is based on the Rif and Rambam.

Gra (DH she'Hu): The Yere'im learns from 74b, which obligates for sewing two stitches only if he tied them. If one is liable for tying even a single knot, he would be liable due to tying! (Damesek Eliezer -we discuss a professional!)

Note: Perhaps he is liable for sewing even if he will untie it after a while, but he is exempt for tying, for it is not permanent! Perhaps the Gra and Yere'im were not concerned for this objection, for the need to tie it is in order that the stitches will last!

Rema (ibid.): However, to avoid pain one need not be concerned, and one may untie it. Chachamim did not decree where there is pain.

Magen Avraham (6): Sefer ha'Zichronos forbids.

Kaf ha'Chayim (26): The Acharonim rules like the Rema. One may be lenient for any need.

Kaf ha'Chayim (28): We do not permit what is not normally untied every day. However, if one normally makes a bow, and he forgot and made a knot, this is like a knot that is untied every day.

Rema (ibid.): We require a double knot [to forbid] only when one ties two things together. A knot in one end of a string is like a double knot.

Gra (DH v'Ha): The source to require a double knot (74b) discusses tying two matters.

Kaf ha'Chayim (23): The Birkei Yosef says that here, no one is stringent about a double knot on the belt. It is an amateur temporary knot. This is when it is not tight.

Kaf ha'Chayim (24): One should not tie a double knot on his belt. (I.e. where people often tie it tightly - PF.) Rather, he ties one knot and a bow. If he forgot and made a double knot and he needs to eliminate, he may untie it. Chachamim did not decree in a situation of pain.

Kaf ha'Chayim (32): Any knot not destined to last a long time, if there is a big need for Shabbos, one may untie it through a Nochri, for this is Shevus of Shevus.

Mishnah Berurah (13): The Beis Meir says that the Shulchan Aruch permits for a Mitzvah, like the Rambam and Tur. Rashi, Tosfos and the Bartenura hold that a Mitzvah does not permit any forbidden knot.

Kaf ha'Chayim (20): Therefore, when possible, one should make only a bow.

Mishnah Berurah (14): The Rif and Rambam forbid any professional knot. We are not experts about this, so presumably, anything tied tightly is [Safek - PF] professional. Therefore, we are careful about any double knot, for this is strong. The Shulchan Aruch says 'any knot' to teach that even the Heterim in this Siman are only for single knots.

Mishnah Berurah (15) and Bi'ur Halachah (DH Dino): Because it gets very tight, it is called a professional knot. Even though Semag does not discuss professional knots, for he does not cite the Rambam, since we see that Semag calls a knot at the end of a thread a Torah knot, just like a regular double knot, the Rema holds that also regarding being a professional knot, it is like a double knot.

Kaf ha'Chayim (9): If a Sefer Torah was tied with a permanent knot, they read in another Sefer, and on another Shabbos they take it out.

Note: Perhaps this means that [during the week they untie it, and] the next Shabbos they read from this Sefer [even though the Sefer used last Shabbos is rolled to the right place, and this one is not], lest people think that they did not read from it because it is Pasul.

Bi'ur Halachah (DH b'Rosh): the same applies to one end of a rope (Semag). The Perush there (R. Eizik Shtein) says similarly about the end of a sewing thread. (The Mordechai explicitly says so.) The Gemara says that one must tie them to liable for sewing, and it does not mention liability for tying, for it discusses tying the two ends together.