Do not tie a professional knot on Shabbos, even if you intend to untie it within 24 hours. (ShA 1)
What classifies as a professional knot? No one knows for sure. So, the poskim say any knot which is tight like a double knot might be a professional one. Even one overhand knot at the end of a string, thread or rope is ossur to tie. (Rama 1 – MB 14)
If the knot is really not professional, there are poskim who hold that you still may not make it intending to last 24 hours. But if you intend to **untie** the knot on the night of Motzoay Shabbos it is permitted to **tie** on Shabbos. (Rama 1 – MB 6)
Why can’t I tie tzitzis on Shabbos with intention to untie it Motzoay Shabbos? Because we ignore your intentions in a case where the knot is usually made for permanence. (BeH “hakoisher”)
Any knot which is forbidden to tie, is not allowed to be untied (even when tied before Shabbos.) Any knot which is allowed to tie on Shabbos can be untied as well. If you can’t manage to untie it, you can snap it apart if need be. Don’t snap it apart in front of an ignorant person. (Rama 1 – MB 7)
It is forbidden to insert the laces into a new pair of shoes. The same goes for a drawstring in a new pair of trousers or the like. Since you want the string to remain in the garment – it’s M’sakain Mona. But to put a belt through the loops is muttar since you will insert and remove the belt all the time. (MB 16)
You aren’t allowed to knot a lace at its end so it won't slip out. Don’t even lace it in a way that you will be tempted to knot the end. (Rama 2 – MB 19, 20)
It is forbidden to detach temporary knots or stitching that close openings in garments. It’s M’sakain Mona. (ShA 3)
Any temporary knot may be untied by instructing a gentile – if there is a great need. Shvus d’shvus l’tzorech harbay. (MB 25)
A bow may be tied on Shabbos even if it’s tight and permanent. Even a double bow is allowed. (ShA 5 – MB 29 – BeH “anivoh”)
A bow tied on top of a single overhand knot is allowed only when you intend to untie it on that day. If you intend to keep the bow tied for more time than that, like by tying a lulav on Yom Tov, it is ossur. (MB 29)
If you intend to tie a bow and accidently it formed a knot, it can be untied – similar to a knot meant to be untied on that same day. (MB 23)
Ropes aren’t muktza. (MB 33)
Twisting threads to make rope is Koshair. Untwisting them could be Mattir. (MB 34)