Auxiliary verbs or helping verbs are called modals.
These words are used to ask for permission, express ability, possibility, etc.
Will/ Would are used to ask to do something or make a suggestion /offer.
Examples: When will you send the email?
Will you open the door ?
Will/ Would are used to express determination or willingness.
Example: I will try to do this sum myself.
Can/ Could are used to express ability
Examples : Can I use your phone?
Can/Could are used to ask and give permission.
Examples: Can/Could you pass the pen?
He can swim like a fish.
Can/Could are also used to make a suggestion.
Examples: You can cook food better than my sister.
I could give you a lift to the station.
May/Might are used to tell, to ask and give permission.
Examples: May I come in?
I might go out tonight.
May /Might are also used to tell that something is likely to happen in future.
Examples: That may be the better solution.
They might move to London.
Needn’t is used to express that it is not necessary to do something.
Shouldn’t is used to suggest that we should not do something.