General Auxiliaire verb

All the auxiliary verbs except be, do and have are called modals. Unlike otherauxiliary 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 

Modal	Example	Uses
Can	They can control their own budgets. We can’t fix it. Can I smoke here? Can you help me?	Ability / Possibility Inability / Impossibility Asking for permission Request
Could	Could I borrow your dictionary? Could you say it again more slowly? We could try to fix it ourselves. I think we could have another Gulf War. He gave up his old job so he could work for us.	Asking for permission. Request Suggestion Future possibility Ability in the past
May	May I have another cup of coffee? China may become a major economic power.	Asking for permission Future possibility
Might	We'd better phone tomorrow, they might be eating their dinner now. They might give us a 10% discount.	Present possibility Future possibility
Must	We must say good-bye now. They mustn’t disrupt the work more than necessary.	Necessity / Obligation Prohibition
Ought to	We ought to employ a professional writer.	Saying what’s right or correct
Shall (More common in the UK than the US)	Shall I help you with your luggage? Shall we say 2.30 then? Shall I do that or will you?	Offer Suggestion Asking what to do
Should	We should sort out this problem at once. I think we should check everything again. Profits should increase next year.	Saying what’s right or correct Recommending action Uncertain prediction
Will	I can’t see any taxis so I’ll walk. I'll do that for you if you like. I’ll get back to you first thing on Monday. Profits will increase next year.	Instant decisions Offer Promise Certain prediction
Would	Would you mind if I brought a colleague with me? Would you pass the salt please? Would you mind waiting a moment? "Would three o`clock suit you?" - "That’d be fine." Would you like to play golf this Friday? "Would you prefer tea or coffee?" - "I’d like tea please."	Asking for permission Request Request Making arrangements Invitation Preferences

!Note The modal auxiliary verbs are always followed by the base form.

The verb used to, which is explained here, can also be used like a modal verb.