|Can is used to express the ability to do something:|
|:: She can speak English very well.|
:: Can Janet play the piano? No, she can't.
:: I can't drive a car.
|Can also expresses the possibility to do something:|
|:: We can go to the concert tonight.|
:: We can play tennis this afternoon.
|May is used to express probability:|
|:: We may go to the park after school.|
:: I may play football with my friends on Sunday.
|May is also used for permissions:|
|:: You may stay here.|
:: May I borrow your pen?
|May is more formal. In informal spoken English we sometimes use can to request permission ("Can I open the window?").|
|We use might as a past form of may and to express probability (= it's very unlikely):|
|:: She said that she might move in the new house.|
:: We might go to the Austria next year.
|Could is used as a past form of can:|
|:: Could you finish your homework last night?|
|We also use could to ask for permission:|
|:: Could I borrow your pen, please?|
:: Could I go out?
|Must is used for strong obligation, recommendation, and conclusion:|
|:: He must clean his room.|
:: I must write an essay.
:: You must see this film.
:: John must be in London now.
|Will is used for asking or ordering somebody to do something:|
|:: Will you help me, please.|
:: You'll wash the dishes now!
|Will is also used to express willingness and intention:|
|:: I'll help you, I promise.|
:: I will call you as soon as I arrive.
|Will is used for talking about or predicting the future:|
|:: I'll tell you what I think about them.|
:: You'll be there in time if you hurry.
:: I'm sure you'll be fine!
|Would is used to make polite request and to give hypothetical advice:|
|:: Would you pass me the salt, please.|
:: If I were you, I would go to the Unated States.
:: I would not (wouldn't) do that.
|We use shall in questions to make offers or suggestions:|
|:: Shall I close the door?|
:: Shall we go to the theatre tonight?
|Should is used to give advise:|
|:: You should do exercises every day.|
:: You should not (shouldn't) smoke.