CAN
1. It is used to express the ability to do something.I can swim very well.
Can he can speak English fluently? - No, he can't.
We cannot sing at all!
2. It expresses the possibility to do something.
We can go to the seaside at last. Our holidays start next week.
3. We use it to say that something is probable.
It can be John. He has blond hair and he is wearing glasses.
4. It expresses the permission to do something.
Why not? You can marry her. She is a nice girl.
MUST
1. It is used for strong obligations.It is personal, because it expresses the speaker's opinion or will.
I must clean my teeth. I want to be healthy.
You must go there. And do it right now!
2. It means a strong recommendation.
You must see it. It's the best film I've ever seen.
3. We use it to show the certainty of the speaker.
They must be at school by now. It's already 9 o'clock.
4. The opposite of must is need not.
Mum, must I wash up? - No, you needn't. I've already done it.
Must not has a different meaning.
It is used to express prohibition that involves the speaker's will.
We mustn't come late today. Or the teacher will be very angry.
He mustn't enter this room. It is dangerous.
HAVE TO
1) In the affirmative: HAVE TO has a meaning similar to MUST.
I have to go to the school.
2) In the negative: HAVE TO has a different meaning: "you don't need to dot that"
It's Sunday! I don't have to go to school.
EXERCISES:
Exercise with Can & Must
Exercise with Cant & Must - Questions
exercise with Can & Must 2
Exercise Can/can't or Must/mustn't
Exercise Can or Must
Exercise Allowed or Not Allowed
Exercise Have to or Must
Permission, obligation, and prohibition
Permission, Ability, Obligation, Advice...
Exercise Must or Have to...
Must, needn't or mustn't
Obligation