The following are the modal auxiliary verbs in English:

Will, would; shall, should; may, might; can, could; must; ought; dare; need

Modal auxiliaries have some common characteristics

1.    They are never used alone.

A modal auxiliary verb is never used alone. A principal verb is either present or implied.

I can knit. (Modal verb – can, principal verb – knit)
He should apologize. (Modal – should, principal verb – apologize)
Will you go? (Modal – will, principal verb – go)
Yes, I will. (Here the principal verb go is not present but it is implied.)

Principal verbs can stand alone.

She knitted a sweater. (Principal verb – knitted)
He apologized. (Principal verb – apologized)
He goes to the factory every day. (Principal verb – goes)

2.    Modal auxiliaries have a single form throughout the present tense, whatever be the number and person of the subject.

Compare:

I can swim.
She can swim.
They can swim.
You can swim.
He may pass.
She may come.

You will have noticed that the modal auxiliary verbs do not change their form according to the number and person of the subject. The primary auxiliaries, on the other hand, change their form according to the number and person of the subject.

She is swimming.
They are swimming.
You are swimming.
I am swimming.
I do agree.
He does agree.
They do agree.
He has agreed to come.
I have agreed to come.

3.    The modal auxiliaries do not have infinitive or participle forms: you cannot say to will, to must or to can. Note that when we say to will, to need or to dare, the verbs will, need and dare are used as principal verbs, and not auxiliaries.

Similarly you cannot add –ing to any of these auxiliaries to make present participles. Modal auxiliaries do not have past participles either. Note that when we say willing, daring or needing, the verbs will, need and dare are used as principal verbs, and not auxiliaries.

The primary auxiliaries, on the other hand, have the infinitive and participle forms.

He was to be promoted.
She seems to have gone.

Here the forms to be and to have are infinitives.

He is being tortured.
Having lost the war, Germany surrendered.

Here the forms is being and having lost are examples of participles.

He has been punished.
I have had my lunch.

Here the forms has been and have had are examples of past participles.

As the modal auxiliaries do not have the infinitive and participle forms, they are sometimes called defective verbs.