The English modal verbs are a subset of the English auxiliary verbs used mostly to express modality (properties such as possibility, obligation, etc.). They can be distinguished from other verbs by their defectiveness (they do not have participle or infinitive forms) and by their neutralization (that they do not take the ending -(e)s in the third-person singular).
The principal English modal verbs are can, could, may, might, shall, should, will, would, and must. Certain other verbs are sometimes classed as modals; these include ought, had better, and (in certain uses) dare and need. Verbs which share only some of the characteristics of the principal modals are sometimes called "quasi-modals", "semi-modals", or "pseudo-modals".
The verbs customarily classed as modals in English have the following properties:
They do not inflect (in the modern language) except insofar as some of them come in present–past (present–preterite) pairs. They do not add the ending -(e)s in the third-person singular (the present-tense modals therefore follow the preterite-present paradigm).
They are defective: they are not used as infinitives or participles (except occasionally in non-standard English; see below), nor as imperatives, nor (in the standard way) as subjunctives.
They function as auxiliary verbs: they modify the modality of another verb, which they govern. This verb generally appears as a bare infinitive, although in some definitions, a modal verb can also govern the to-infinitive (as in the case of ought).
They have the syntactic properties associated with auxiliary verbs in English, principally that they can undergo subject–auxiliary inversion (in questions, for example) and can be negated by the appending of not after the verb.
The following verbs have all of the above properties, and can be classed as the principal modal verbs of English. They are listed here in present–preterite pairs where applicable:
can and could
may and might
shall and should
will and would
must (no preterite; see etymology below)
Note that the preterite forms are not necessarily used to refer to past time, and in some cases, they are near-synonyms to the present forms.