Both must and must not express obligations, in fact opposite ones. To express there is no obligation you can use do not have to. Or you can use noun must, e.g:
There is no such must.
Negated form, must not, has different meaning than do not have to. Consider modal verbs: can, may, have to etc. Negative forms of these modals have meaning that there is no obligation. In this sense, the meaning of must't seems odd, counterintuitive, esp. for a new learner. However, in some contexts, using must / mustn't is more useful than have to / do not have to and vice versa.
For example, must / mustn't is useful in exact/provable contexts like mathematics, logic. E.g., given the statement A is B, i.e. A must be B, if one disproves it then the disproval implies the opposite: A isn't B, i.e. A mustn't be B. In fact, in contemporary use: Must and must not are often used in deductions, e.g. for must see (merriam-webster.com/dictionary/must), points 4,5 or (collinsdictionary.com/dictionary/english/must_1), point 4.
Another example where the meaning of modal mustn't is useful is in detailed instructions, manuals, highway code, legal regulations (https://www.merriam-webster.com/dictionary/must), points 1,2,3. In such cases there is important to list obligations, steps how to proceed, and then do no have to is not useful. E.g. You must proceed when you are given green light but you mustn't when there is red light.