must vs don't have to vs must not

[keannu]

When thinking of "must", "don't have to", "must not", many grammar books say the opposite of "must" is "don't have to", not "must not". "must not" is just a negative obligation. But it's kind of confusing even though I know "must not" is a parallel obligation with "must", but also seems the opposite of "must" considering the degree of obligation. I don't know how to tell the three. Which is which's opposite?

ex1)You must go <=> You don't have to go
You must not go

[5jj]

You must go / You have to go - There is a positive obligation to go.
You must not go - There is a positive obligation to not-go.
You don't have to go / you needn't go - There is no obligation to go (but you can if you want to).
You may go (formal) - You have permission to go.
You may not go (formal) You are not permitted to go. You are forbidden to go.