Review Modal verbs by function here
Prohibition (Must not)
Deduction and certainty
"Must" is commonly used to express obligation, similar to "have to". Many text books explain the possible difference between the two as internal (must) and external (have to) obligation. Perhaps a better way to think about it is an obligation we agree with (must) and an obligation imposed upon us (have to)
We must prepare dinner before they arrive
You must wear your seatbelt in the car
Tickets must be retained for inspection
We DO NOT use "must" to talk about obligation in the past. To talk about that we use "Had to".
The negative form is used to talk about things that are prohibited, not permitted, not allowed. This is different to the negative of Have to (Don't have to) which expresses a lack of obligation.
"Must not" is a form of talking about things that are not allowed, or prohibition:
You must not drink and drive
He must not have an ice cream
It is very common to see this structure in notices and public instructions:
Passengers must not cross the yellow line
Luggage must not be left unattended
Deduction & Certainty
We often use "must" when we have considered a situation and come to a conclusion based on the evidence we have observed, known as deduction:
He must be exhausted after all that running
They must be devastated, they worked so hard to refurbish the house and then a freak storm destroyed it.
This function can also be used to talk about deductions on past events using "must" + have + participle
He must have taken the train becuase if he had driven he would be here by now
They must have decided to change house some time ago
We must have left the presents in the car
We sometimes use "must" to encourage someone to do something (sometimes considered strong advice) or make an invitation:
You must come and visit soon
You must try some of this meatloaf, it is wonderful!
You must see them play live, it is an unforgettable experience.
When we wish to express criticism of behaviour, we can use "must" in a question form to do so:
Must you eat with your mouth open?
Must you always come home so late?