All the auxiliary verbs except be, do and have are called modals. Unlike other auxiliary verbs, modals only exist in their helping form; they cannot act alone as the main verb in a sentence.
The modal verbs are :
can : can you help me ?
could : could I borrow your dictionary?
may : may I have another cup of coffee?
might : They might give us a 10% discount
must : we must obey our elders
shall : shall I help you with your luggage?
should : I think we should check everything again
ought to : We ought to employ a professional writer
will : I 'll get back to you first thing on Monday
would : Would you mind waiting a moment ?