Modal verbs
All the auxiliary verbs except be, do and have are called modals. Unlike other auxiliary verbs modals only exist in their helping form; they cannot act alone as the main verb in a sentence.
Be, do, and have also differ from the other auxiliaries in that they can also serve as ordinary verbs in a given sentence.
The modal verbs are:-
CAN / COULD / MAY / MIGHT / MUST / SHALL / SHOULD / OUGHT TO / WILL / WOULD

The uses of the modal verb can:
They can control their own budgets…………………… Ability / Possibility
We can’t fix it. …………………… Inability / Impossibility
Can I smoke here? …………………… Asking for permission
Can you help me?...........Request

The uses of could:
Could I borrow your dictionary? …Asking for permission
Could you say it again more slowly? ……Request
We could try to fix it ourselves. ……Suggestion
I think we could have another Gulf War……Future possibility
She could play the piano when she was two…Ability in the past

The uses of May
May I have another cup of coffee? ……… Asking for permission
China may become a major economic power… Future possibility

The uses of Might
We'd better phone tomorrow, they might be eating their dinner now. … Present possibility
They might give us a 10% discount…future possibility
The uses of Must
We must say good-bye now. ..necessity/ obligation

They mustn’t disrupt the work more than necessary…prohibition

The uses of Ought to
We ought to employ a professional writer…saying what’s right or correct.

The uses of Shall
(More common in the UK than the US)
Shall I help you with your luggage? …Offer
Shall we say 2.30 then? …suggestion
Shall I do that or will you?.....Asking what to do

The uses of Should
We should sort out this problem at once. ….saying what’s right or correct
I think we should check everything again. …..recommending action
Profits should increase next year…uncertain prediction


The uses of Will
I can’t see any taxis so I’ll walk. ..Instant decision
I'll do that for you if you like. …offer
I’ll get back to you first thing on Monday. ..Promise
Profits will increase next year….Certain prediction

The uses of Would
Would you mind if I brought a colleague with me? ..asking for permission
Would you pass the salt please? …..request
Would you mind waiting a moment? ….request
"Would three o`clock suit you?" - "That’d be fine." …Making arrangement
Would you like to play golf this Friday? …invitation
"Would you prefer tea or coffee?" - "I’d like tea please."….Preferences