Modal verbs can be used to express the following:
Possibility
– That could/might/may be the answer.
– The thief could/might/may have had a knife.
– I can’t have been more than two at the time.
Logical deduction
– That must be Tom at the phone.
– It can’t be Susie’s dress – she never wears pink.
– The applicant must have performed very well at the interview to get the job.
Obligation/necessity
– You must leave the building immediately.
– I‘ve got to finish this report today.
– They had to record everything they did.
Lack of obligation/necessity
– You don’t have to get a visa.
– We didn’t need to pay to go in.
– We needn’t have bothered to book seats.
Prohibition
– You mustn’t leave your mobile phone switched on during lessons.
Advice (weak obligation)
– You should try to bring as little luggage as possible.
– You ought not to be playing music so late at night.
– They should have/ought to have taken out insurance.
Permission
– Can I borrow your dictionary?
– May I open the window?
– I asked if I could take some time off work.
Ability
– They can all speak several languages.
– I was afraid of the water because I couldn’t swim.