modal auxiliary verb
We have ten modal auxiliary verbs: can, could, may, might, must, ought to, shall, should, will, and would. We use them to express the mood of the verb, which, most often, is the indicative mood (expressing something as a fact). The modals enable us to express obligation, necessity, permission, or certain conditional actions, as in I might write the book.
Notice that these words lack principal parts. For example, there is no past participle or present participle for these modal verbs. The word can does have could to express a sense of the past, but none of these words have traditional principal parts (infinitive, past tense, past participle, present participle). For example, there's no such expression as “to must.” Also, none of the modals may act as main verbs.
Often writers will drop a main verb when it's clear what the modal refers to. You should, too. See how it works?
Other auxiliary verbs—to be, have, and do—do have meanings as main verbs.
See primary auxiliary verb.