Can – Could – (be) able to
To show ability
To suggest a possibility or to give an option
To ask for or to give permission
To show impossibility
I can run 10 miles.
I could run 10 miles when I was in high school.
May – Might
To ask for or to give permission (formal)
To show possibility
The instructor may come to class late today.
The instructor might have come to class late yesterday.
Must – have/has/had to
To show necessity
To show lack of necessity
I am glad that I don’t have to cook tonight.
We had better leave. It is getting late.
Will – Would – (be) going to
To indicate future time
To make a promise or to show willingness
To state a general truth
To ask a polite question
The federal government will provide assistance to the hurricane victims.
Mark promised that he would help me with my math homework.
Shall – Should – Ought to
To show advisability
To show advisability after the fact
To show obligation
To show an obligation that was not carried out
To show expectation
To show an expectation that was not realized
I should renew my driver’s license. It expires next month
You ought to receive my letter in two days.