MODAL AUXLARIES

MODAL AUXLARIES?
The verbs can, could, will, would, should, may, might, must, ought and shall are verbs which 'help' other verbs to express a meaning: it is important to realise that these "modal verbs" have no meaning by themselves. A modal verb such as would has several varying functions; it can be used, for example, to help verbs express ideas about the past, the present and the future. It is therefore wrong to simply believe that "would is the past of will": it is many other things.

Explanation	Sample sentences
Do not use modals for things which happen definitely.	The sun rises in the east. - A modal can't be used in this sentence.
They have no -s in the 3rd person singular.	He can play football.
Questions are formed without do/does/did.	Can he speak Spanish?
It follows a main verb in its infinitive.	They must read the book.
There are no past forms (except could and would).	He was allowed to watch the film.
When you use the past participle you tell about things which did not happen in the past.	You should have told me.

Long and contracted forms of modals

Affirmative		Negative
Long forms	Contracted forms	Long forms	Contracted forms
can	--	cannot	can't
could	--	could not	couldn't
may	--	may not	--
might	--	might not	--
ought to	--	ought not to	oughtn't to
need	--	need not	needn't
shall	'll	shall not	shan't
should	'd	should not	shouldn't
will	'll	will not	won't
would	'd	would not	wouldn't

CAN & COULD

Talking about ability

Can you speak Mandarin? (present)
She could play the piano when she was five. (past)

Making requests

Can you give me a ring at about 10? 
Could you speak up a bit please? (slightly more formal, polite or 'softer')

Asking permission

Can I ask you a question?
Could I ask you a personal question? (more formal, polite or indirect)

Reported speech

Could is used as the past of can.

He asked me if I could pick him up after work.

General possibility

You can drive when you're 17. (present)
Women couldn't vote until just after the First World War.

Choice and opportunities

If you want some help with your writing, you can come to classes, or you can get some 1:1 help.
We could go to Stratford tomorrow, but the forecast's not brilliant. (less definite)

Future probability

Could (NOT can) is sometimes used in the same way as might or may, often indicating something less definite.

When I leave university I might travel around a bit, I might do an MA or I suppose I could even get a job.

Present possibility

I think you could be right you know. (NOT can)
That can't be the right answer, it just doesn't make sense.

Past possibility

If I'd known the lecture had been cancelled, I could have stayed in bed longer.

MAY

Talking about things that can happen in certain situations

If the monitors are used in poorly lit places, some users may experience headaches.
Each nurse may be responsible for up to twenty patients.

With a similar meaning to although

The experiment may have been a success, but there is still a lot of work to be done. (= Although it was a success, there is still ...)

MIGHT

Saying that something was possible, but did not actually happen

You saw me standing at the bus stop! You might have stopped and given me a lift!

OUGHT TO

Ought to usually has the same meaning as should, particularly in affirmative statements in the present:

You should/ought to get your hair cut.

SHALL

Shall is a form of will, used mostly in the first person. Its use, however, is decreasing, and in any case in spoken English it would be contracted to "-ll" and be indistinguishable from will.

The only time you do need to use it is in questions, when:

Making offers

Shall I fetch you another glass of wine?

Making suggestions

Shall we go to the cinema tonight?

SHOULD

Giving advice

I think you should go for the Alfa rather than the Audi.
You shouldn't be drinking if you're on antibiotics.
You shouldn't have ordered that chocolate dessert - you're not going to finish it.

Obligation: weak form of must

The university should provide more sports facilities.
The equipment should be inspected regularly.

Deduction

The letter should get to you tomorrow - I posted it first class.

Things which didn't or may/may not have happened

I should have renewed my TV licence last month, but I forgot.
You shouldn't have spent so much time on that first question.

WILL

Talking about the past with certainty
I'm sure you will have noticed that attendance has fallen sharply.

WOULD

As the past of will, for example in indirect speech

"The next meeting will be in a month's time" becomes
He said the next meeting would be in a month's time.

Polite requests and offers (a 'softer' form of will)

Would you like another cup of tea?
Would you give me a ring after lunch?
I'd like the roast duck, please.

SOURCE:LINK 1

          LINK 2