We use must: To express obligation, necessity and duty. You must wear a helmet when riding a motorcycle.( You have to wear a helmet.) To express that it is necessary to do sth. I must water the plants. (It's necessary.) For positive logical assumptions. She must be an actress. I've seen her on TV. (I'm sure she's an actress.)

We use can't for negative logical assumptions. Jack and Paul can't be strangers. They've been next door neighbours for years. ( I'm sure they aren't strangers.)

We use mustn't /can't for prohibitions. You mustn't /can't park your car near a bus stop. ( it is forbidden to park there.)

We use have to to express that it is necessary to do sth ( especially when somebody else other than the speaker has made the decision.) I have to stay late at work tomorrow. ( My boss told me to stay.)

We use don't have to/ needn't to express lack of necessity. I don't have to / needn't do the shopping. I've already done it. ( It isn't necessary for you to do it.)

We use can/ could /may/ might to ask for permission. Could /May /Might are more formal than can. Can I go to the park? Could /may/Might I take next Monday off? ( Is it permitted for me to…?)

We use can / may to give permission. May is more formal than can. Of course you can use the phone. You may leave your luggage here, sir. (You are allowed to…)

We use can't/ mustn't /may not to refuse permission. May not is formal. f.E. I'm afraid you can't stay late tonight. You mustn't watch TV after 9pm. You may not write in ink during the test. ( You aren't allowed to…)

We use could /may /might to show that something is possible or likely. f.E Tom could/ may /might still be at school. ( It is possible that he is still at school.)

WE use would /could/ can to make a request. f.E Could you open the door for me, please?