In British English, both must and have to can be used to talk about necessity and obligation. Americans usually use have to, especially in speech.
I must reach home before 6 o’clock.
OR I have to reach home before 6 o’clock.
Note that must is usually used to talk about obligations that arise from the feelings and wishes of the speaker or the listener.
I must go home. (Because I want to go home.)
You must quit smoking.
Have to is usually used to talk about obligations that come from laws, regulations, arrangements and other people’s orders.
I have got toothache. I must make an appointment with the dentist. (Speaker’s wish)
I can’t come to your party because I have got to see the dentist at 6 o’clock. (A pre-existing arrangement)
To talk about future obligations we can use will have to or have go to.
I have got to be there at 9 o’clock.
After you finish your graduation, you will have to find a job.
Must can be used to give instructions for the future.
You can go out if you want to but you must be back before 10 pm.
Although must and have to express similar ideas, the negatives must not and do not have to / have not got to have quite different meanings.
Must not is used to prohibit. Do not have to is used to say that there is no obligation.
You must not go. (= Don’t go.)
You don’t have to go. (= You can go if you want to but it is not necessary.)