There is another kind of auxiliary verb. This is called a modal auxiliary verb or simply known as «the 9 modal verbs».
They are;
can, could, may, might, must, shall, should, will, and would.
MODAL VERBS express many things such as;
ABILITY can / could
PERMISSION can / could / may
ADVICE / SUGGESTIONS could
OBLIGATIONS must / mustn’t
POSSIBILITY might / may / could
UNCERTAINTY / CERTAINTY must not / must
WILLINGNESS / REFUSAL wouldn’t
REQUEST / OFFER will / shall / could / would / can
POSSIBLE OR IMPOSSIBLE could / could not / couldn’t
QUESTIONS. can i ? could i ? may i ?
INVITATIONS AND OFFERS. would / shall / can