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From Teflpedia

Must is an English full modal verb that expresses obligation.[1]

Must is both the base form and the preterite. When used in the present tense, the present tense modals can,will and may can be substituted, whereas when it’s used in the past perfect, could, would and might can be substituted. Its behaviour is rather weird, as it has present simple and past perfect uses, but unlike other modal verbs tends not to be used in the past simple.

In the present simple, must expresses obligation - "you must do your homework", and in the negative expresses prohibition, e.g. "you mustn’t smoke in the kitchen.” Though need to and have to are similar in meaning to must, “don’t have to" and “don’t need to" are different, as someone is not obliged.

In the past perfect, e.g. "they must have gone shopping" - it expresses deduction.

In the past simple, we tend not to use must but tend to use "had to"/"needed to" (positive) or “couldn’t"/"weren’t allowed to" (negative). e.g. *“When I was at school, we mustn’t smoke", but “When I was at school we weren’t allowed to smoke.”

Must can also be used as a noun, e.g. This is a must.

In the present perfect, is it comparable to will/may/can? Not sure.

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