Modal auxiliary verbs are used to moderate the main verb, that is to enhance or restrict the verb to a certain context.
The most common modal auxiliaries in English are:

can

could may

should might

will must

would

Notice the usage of modals in the following sentences:

I pay my taxes. General declaration of fact. Paying taxes is something I normally do.

I can pay my taxes. Expresses ability. I have the means (funds) to pay.

I might pay my taxes. Expresses possibility, but not certainty. Maybe I will pay; maybe I won't.

I will pay my taxes. Expresses future intent. I resolve to do it at some later time.

I should pay my taxes. Expresses mild obligation. It is required, and I expect to comply.

I could pay my taxes. Expresses possibility. If I have nothing else to do with the money, I might pay taxes.

I would pay my taxes. (In this case), expresses reservation. If I had the money (but I don't). . .

I must pay my taxes. Expresses strong obligation. I am required and have to comply.

Modals are followed by only the base form of the verb and are not used alone unless there is a clear connection to a main verb.

He must to finish his homework. Not ok
He must finish his homework.Ok

Jack could heard the bell.Not Ok

Jack could hear the bell. Ok

Penny will going to the movie.Not Ok

Penny will go to the movie.Ok

There are many ways to make requests in English. The most common involves using the imperative and modals. See the examples below:

Using the Imperative

The imperative is the simple form of the verb. The
subject of an imperative sentence is understood as "you" although it is usually not spoken.

Open the door.
Will you help me?

Pick up your toys.

Please help me.
(You) open the door.
Yes, I will (help you).

(You) pick up your toys.

(You) please help me.

The imperative is often used by persons of authority when speaking to subordinates, e.g. parent to child.

Using Modals

To show respect and politeness, most people use modal
expressions when making requests. For example:

Will you...?
Would you...?

Would you please...?

Could you (please)...?

Could you possibly...?

Would you kindly...?

Would you mind (Ving )...?

Would you be so kind as to...?
Will you open the door for me?
Would you open the door for me?

Would you please open the door (for me)?

Could you (please)...? Could you (please) open the door?

Could you possibly open the door?

Would you kindly open the door?

Would you mind opening the door?

Would you be so kind as to open the door?

Common Problems with Modals

1. Using "to" unnecessarily:

Incorrect
They going to meet us at the theater.

He should to eat his dinner.

I had better to go now.

You must not to use that pencil.

Correct
They are going to meet us at the theater.

He should eat his dinner.

I had better go now.

You must not use that pencil.

2. Using anything but the base form after a modal:
John could heard the bell.
Penny will going to the movie.
John could hear the bell.
Penny will go to the movie.

3. Using double modals:
You should ought to speak English.
She might can help me.
You ought to speak English. /should speak
She might be able to help me.

4. Omitting "be" in certain modal expressions:
They going to meet us at the theater.
Jack supposed to take his medicine.
They are going to meet us at the theater.

Jack is supposed to take his medicine.

5. Using wrong word order in questions:
How I can help you? Not ok
Where I should go for the meeting?Not ok
How can I help you? OK
Where should I go for the meeting?OK

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