Biblically:

It is only Biblically prohibited to tie or untie a knot if:

1. At the time of making it one plans to let the knot remain tied for as long as it can possibly last and does not plan to ever untie it.[1]
2. According to some opinions there must also be fulfilled: That the knot is strong and tough similar to the knots that professionals make in their labor.[2]

Rabinically:

It is Rabinically forbidden to tie or untie any knot that:

1. Is made in a professional manner even if not meant to last at all [even in a scenario that involves pain].[3]Or
2. Is meant to last temporarily, meaning that one has in mind a set time by when he will undo the knot, and this set time is past 24 hours from when the knot has been made.Or
3. The knot is a type of knot that is at times left to last forever, then it is forbidden to tie it.[4]

Permitted:

It is permitted to tie and untie any knot which is:

1. Any knot which is only Rabbinically forbidden to tie and untie [i.e. any knot which one has a set date to untie] may be tied for the sake of a Mitzvah.[5]Or
2. If not needed for the sake of a Mitzvah then it is permitted if all the following conditions are fulfilled:

1. The knot is not meant to last for 24 hours. In time of need if it is meant to last for 24 hours , but for less than 7 days, then one may tie or untie it through a gentile[6]And
2. It is not a professional knot.And
3. The knot is never usually left to last forever.[7] 

   And

4. It is not the first time that this knot is being open or is but does not make a finishing touch to the vessel. If it does then it is forbidden due to Fixing a vessel.[8]