Uses of auxiliary verbs

To make negative statements

In modern English, the simple addition of not is not enough to form negative statements.

Study the following sentences.

You know him. (Affirmative)
You do not know him. (Negative)
(NOT You know not him.)

We waited for them. (Affirmative)
We did not wait for them. (Negative)
(NOT We waited not for them.)

In modern English, the auxiliaries are the only verbs which can form their negatives by the simple addition of not.

Will you come?
I will not. OR I won’t.
Can I do it?
You cannot. OR You can’t.

The auxiliaries are also the only verbs which can be used along with the shortened form of not.

Will not = won’t
Cannot = can’t
Should not = shouldn’t

To form questions

A question is usually formed by putting an auxiliary verb before the subject of the sentence.

He is a nice fellow.
Is he a nice fellow?
They have won the race.
Have they won the race?

Note that the auxiliaries are the only verbs that can thus be inverted with the subject. In the case of other finite verbs, the auxiliary do and its forms are used.

He fell off the ladder.
Did he fall off the ladder? (NOT Fell he off the ladder?)
They went to Mumbai.
Did they go to Mumbai? (NOT Went they to Mumbai?)
They make good cheese.
Do they make good cheese? (NOT Make they good cheese?)