There are 3 different categories of knots. Knots made to last forever that are forbidden Biblically. Knots that are made to untie on the same day that are permitted. Knots made to last for a while but not forever that are forbidden Rabbinically.

Women would wear garment with knots that tied over the shoulders- those are permitted to make on Shabbos bc they’re made to unite that day. We’re not concerned with possibility that she’ll only undo one of the two straps and slip the garment off without untying both.

Knot made on hat is permitted to tie on Shabbos. Even if the hats loose were not concerned the woman may just pull off the hat without untying the knot.

Fine people tie shoelaces tight and making knots is therefore permitted on Shabbos bc it’s made to be untied that day when one takes off the shoe. Students at the yeshiva would tie their shoes very loosely and undo the knots only once a week so they can’t tie those knots on Shabbos.

Strap on sandals is generally forbidden to make in Shabbos bc it’s knot that’s made to last, but a sandal used by two different people with different sized feet may be adjusted on Shabbos bc it’s not made to last.

The sandals had two leather straps- one on the outside and one on the inside, between ones legs. If the inner one would break, they would fix it. If the outer one break, although it was possible to fix it, they didn’t do it, bc the repair was noticeable and unbecoming. So R Yehuda holds that if the outer strap broke, the sandal is no longer considered a shoe. It would lose tumah it previously contracted, it would be muktzeh on Shabbos, and it could not be used for Chalitza. However, the Rabanan disagree and still consider it a shoe bc one could made it into the sandal for the other foot, where the outside would become the inside and the repair wouldn’t be as noticeable. Acc to the Rabbis, it still has contracted tumah, it’s not muktzeh, and it may be be used for Chalitza.

There’s a concept of פנים חדשות. If too many repairs are done to a kli it’s no longer the same kli. If a kli Gets many small holes that one keeps on sealing it loses an old tumah once the seals are the size of a pomegranate. Even though the kli at no point had a hole the size of a pomegranate, it’s a new kli with all the seals so it loses previous tumah.

R Yochanan is praised as being like an angel for introducing this concept of פנים חדשות.