an auxiliary verb

used to express intention, necessity, obligation, offer, permission, possibility, prohibition, question, request, suggestion

cannot function as a main verb in a sentence

She can finish doing the dishes. (possibility)

Can we take more of these? (permission)

Can you wash my car? (request)

Could I borrow your car? (permission)

I think we could get a woman president. (possibility)

Could you eat your food in the dining room? (request)

You could try finding another job. (suggestion)

May I see the menu please? (permission)

It may rain tomorrow. (possibility)

They might give us free tickets. (possibility)

We must go home now. (necessity, obligation)

They must not be win the game this weekend. (prohibition)

We must go home now. (necessity, obligation)

We ought to move to another city. (suggestion)

Shall we close the account for you? (offer)

Shall we go out to lunch now? (suggestion)

Shall we go out to lunch or out to dinner? (question)

We should really talk about this. (suggestion)

Profits should increase next year. (prediction)

You will do your homework tonight. (necessity)

Will you go to the party this weekend? (question)

Would you like me to hold that for you? (offer)

You would really like this sushi. (suggestion)