THE MODAL VERBS OF OBLIGATION

We can use have to + infinitive, must + infinitive and should + infinitive to express obligation (something you have to do).

Present	Positive	Negative
have to / don't have to	strong obligation (possibly from outside) -Children have to go to school. (sometimes 'have got to')	no obligation -I don't have to work on Sundays. -You don't have to eat anything you don't like.
must / mustn't	strong obligation (possibly based on the speaker's opinion) -I must study today.	negative obligation -You mustn't smoke here.
should / shouldn't	mild obligation or advice -You should save some money.	mild negative obligation or advice -You shouldn't smoke so much.

Be careful about the difference between mustn't and don't have to!
Mustn't means it's not allowed, or it's a bad idea:

-You mustn't eat so much chocolate, you'll be sick

Don't have to means you don't need to do something, but it's fine if you want to do it:

I don't have to get up early at the weekend (of course, if I want to get up early, that's fine, but I can stay in bed if I want).

Past	Positive	Negative
had to / didn't have to	obligation in the past -I had to wear a school uniform when I was a child.	no obligation in the past -We didn't have to go to school on Saturdays.
must*	changes to 'had to'	-
should have + pp / shouldn't have + pp	a past action which didn't happen: the advice / regret is too late -You should have gone to bed earlier, now you have missed the train.	a past action which didn't happen: the advice / regret is too late -You shouldn't have taken that job., it was a bad idea.

* Remember 'must have done' is a modal verb of deduction or speculation, not obligation in the past. For example: Julie must have left. Her coat's not here.