Modals of English Grammar

Modals are those verbs that express the mode of action by the main verb.

Family of modals

Can, could, may, might, must, ought to, need, dare, will, shall, would, should.  

Can

The modal can indicates possibility or ability:

I can speak English fluently. 

It can get very hot in Arizona.

I can solve this question.

In questions, the modal can requests permission to do something or to ask about possibilities:

Can I go to the cinema?

You can co for a picnic now.

Can Mike come over for dinner? 

Who can answer the next question? When can we get back the results?

Could

Could indicate possibility or ability in the past:

I could have told you that. 

It could have been a disaster.

When I was young, I could run very fast.

Could speculate about future possibilities. In the following examples could and might are synonymous.

It could / might rain tonight.

That could / might be dangerous.

In yes-no questions, could speculates about present possibilities:

Could she be the murderer? 

Could this be a mistake?

It can also make a request. In these examples could and can are synonomous, but could is more polite.

Could / Can you open your window? 

Could / Can you help me move this sofa?

Could indicate an option:

We could go see a video. 

I could become an engineer.

The modal could is also used to form the conditional. The conditional contains an if clause and a result clause. Could is placed in the result clause.

In these examples, could express hypothetical situations:

If I had time, I could play tennis with you.

We could study together, if you want to.

If it weren't raining, we could go on a picnic.

Could mention something that didn't happen because a certain condition was not met:

If we had left sooner, we could have taken the train. 

I could have passed the exam if I had studied more.

I'm glad we took umbrellas. We could have gotten soaked.

Shall and Will the modals shall/will + main verb are used to create future tenses. These modals indicate an intention or an action that is expected to happen in the future.

I will / shall close the door for you. 

Raj will / shall meet us at the train station.

They will / shall leave tomorrow at 4:00.

In wh- questions, shall and will ask about options.

Who will / shall drive the bus? When will / shall I see you again?

How will / shall you get there? What time will / shall we meet?

In yes-no questions, shall and will have different meanings.

Will asks a favor.

Will / Shall you turn off the radio?

Will / Shall you stop machine?

Will / Shall you go with me?

Will also asks for information or knowledge about somebody or something.

Will / Shall Raj ever pay you back?

Will / Shall Mars be visited by humans within twenty years?

Will / Shall you be finished soon?

Shall asks about a preference. In these examples, shall and should are synonymous. 

shall is rarely used; when it is, it's only in the first person singular and plural.

Should / Shall I close the door? Should / Shall he close the door?

Should / Shall I come back later?

Should / Shall Raj bring food to the party?

Should / Shall we stay there?

May and Might

The modals may and might indicate an uncertain future action. These two modals are synonymous.

I may / might stay at home. 

This may / might be a bad idea.

It may / might rain tonight.

May or can give instructions or permission.

You may/can now board the airplane. You may/can begin the exam within ten minutes.

In yes-no questions that make a request, you can use May or can. May is more polite.

May/Can I help you?

May/Can we have some more water, please?

You can might in place of may  or can, but this is extremely rare in American English.

May / Can / Might I be of some assistance? 

May / Can / Might we offer you a proposal?

Must
The modal must indicates an obligation.

You must see this video. 

Raj must see a engineer immediately.

Must also indicate an assumption or probability.

My watch must be broken. 

He must have done that before moving to Spain.

In wh- questions, must is an obligation and can be replaced with the modal should. 

should is much more common in these types of questions.

When should / must we be there? 

Who should / must I talk to?

Must can sometimes form rhetorical questions, when you want the person to stop doing something.

Must you make so much noise?	=	Please be quiet.
Must he ask so many questions?	=	I hope he stops asking questions.

Should and Ought (to)

The modals should and ought to indicate an obligation. These two modals are synonymous.

You should / ought to call your sister. 

I should / ought to go office now.

When used in questions, should ask if an obligation exists.

Should you call her? 

Should we pay now?

 When should we leave? 

What should I wear?

Would

Would followed by like is a polite way of stating a preference.

I would like white wine with my fish. 

We would like a room with a view.

In questions, would + subject + like is a polite request for a choice to be made.

Would you like soup or salad with your meal?

Where would you like to eat dinner?

When would Raj like this delivered?

Would can make a request sound more polite.

Come here!	Would you come here?
Stop making that noise!	Would you stop making that noise?

Would explain an action as a result of a supposed or real condition.

I would go with you if I didn't have to work.

If I had not had to work, I would have gone with you.

She would be surprised if you came to the party.

Raj would drive, but he doesn't have a license.

Would introduce habitual actions in the past.

When I was a trainer, I would go swimming every day. When raj lived in India, 

he would write me long letters.