Expressing ability Terry is twenty years old. He can drive a car. ( present ) When he was ten , he could / was able to ride a bicycle. ( past repeated action) Paula was able to climb to the top of the mountain. ( managed to do ; past single action )
Expressing lack of ability Sue can't dance. ( present ) He couldn't / wasn't able to play chess when he was younger . ( past repeated action ) She couldn't / wasn't able to finish the book.( past single action )
Expressing obligation / duty / necessity You must attend the meeting . ( You are obliged to / You have to / You need to / It is necessary.) must attend the meeting . ( I have decided.) I have to attend the meeting . ( Someone else has decided.) We ought to / should respect the elderly.( less strong than must) Need I buy her a present ? ( Is it necessary ? )
Expressing absence of necessity She doesn't need to / doesn't have to / needn't do the shopping. I'll do it later. ( It isn't necessary.) She didn't need to / didn't have to do the shopping as I had already done it.( It wasn't necessary for her to do it.) She needn't have done the shopping. ( It wasn't necessary for her to do the shopping , but she did.)
Expressing prohibition You mustn't / can't be late for work. ( it's forbidden / you aren't allowed to / it's against the rules / law)
Expressing certainty He must be at home . ( positive ; I'm sure he is.) He can't be sleeping . ( negative ; I'm sure he isn't.)
Expressing probability He ought to / should be in now.( He is probably in.)
Expressing possibility It can get very hot in July . (it is theoretically possible ) We could / may / might be a little late. ( it is possible ) He could / might have been injured. ( but he wasn't )