A verb like be, have and do which is used with another verb to make tenses, passive forms, questions and negatives.
English auxiliaries are divided into two types: the primary auxiliaries be, have and do, and the modal auxiliaries can, could, will, would, shall, should, may, might, must and ought (to). Need and dare are semi auxiliaries. They behave sometimes like modals but at other times like ordinary verbs.
Be (is, am, are, was and were) is added to other verbs to make progressive and passive forms.
I am writing.
Is it raining?
Are you coming with us?
She was punished for lying.
Do is used to make questions, negatives and emphatic forms of non-auxiliary verbs.
Do you smoke?
It doesn’t matter.
Do come in.
Have is used to make perfect tenses.
I have written a novel.
He has agreed to come.
What have you done?
Modal auxiliaries are used with other verbs to add various meanings, mostly to do with degrees of certainty or obligation.