Primary auxiliaries are used to form various tense forms.

She is writing. (Here the primary auxiliary is combines with the -ing form ‘writing’ to form the present continuous tense.)

He has returned. (Here the primary auxiliary has combines with the past participle ‘returned’ to form the present perfect tense.)

Auxiliaries are used in short answers to avoid repetition.

‘Do you love me?’ ‘Yes, I do.’

‘Have you seen a kangaroo?’ ‘No, I haven’t.’

‘Can you sing?’ ‘No, I can’t.’

‘Will she come?’ ‘No, she won’t.’

Auxiliaries are used to form question tags.

She will dance, won’t she?

He doesn’t know the answer, does he?

She will come, won’t she?

He didn’t play well, did he?

My son plays well, doesn’t he?

Modal auxiliaries are used with infinitives (without to) to indicate ideas such as certainty, possibility, obligation, necessity, permission, ability etc.

I will help you. (Promise)

She will come. (Certainty)

We should help him. (Obligation)

He must go. (Strong obligation)

They may come. (Possibility)

They might come. (Weak possibility)

She can speak Tamil. (Ability)

She could write when she was two. (Past ability)

He ought to be here soon. (Obligation)

We need not wait for him. (Lack of necessity)

We should help the poor and the needy. (Obligation)

She should be here soon. (Probability)