The modal auxiliaries are as follows:
Each of these is treated here separately.
Its more common use, however, is to convey the conditional mood, especially in counterfactual conditionals; that is, to express what would be the case if something were different: "If they wanted to do it, they would have done it by now." There is not always an explicit protasis ("if" clause) in this use: "Someone who likes red and hates yellow would probably prefer strawberries to bananas" means the same as, "If someone liked red and hated yellow, he or she would probably prefer strawberries to bananas."
Would can also be used with no modal or temporal meaning, to affect either politeness or formality of speech:
All of these uses can be described as displaying remoteness: either remoteness of time (the past), remoteness of possibility (a conditional), or remoteness of relationship to the addressee (politeness or formality).
Shall derives from a main verb meaning to owe, and in dialects that use both shall and will, it is often used in instances where an obligation, rather than an intention, is expressed.
Should is to shall as would is to will, except that should is common even in dialects where shall is not.
In some dialects, it is common to form the subjunctive mood by using should: "It is important that the law should be passed" (where other dialects would say, "It is important that the law be passed") or "If it should happen, we are prepared for it" (or "Should it happen, we are prepared for it"; where early Modern English would say, "If it happen, we are prepared for it," and many dialects of today would say, "If it happens, we are prepared for it").
Should commonly describes an ideal behavior or occurrence and imparts a normative meaning to the sentence; for example, "You should never lie" means roughly, "If you always behaved perfectly, you would never lie"; and "If this works, you should not feel a thing" means roughly, "I hope this will work. If it does, you will not feel a thing." In dialects that use shall commonly, however, this restriction does not apply; for example, a speaker of such a dialect might say, "If I failed that test, I think I should cry," meaning the same thing as, "If I failed that test, I think I would cry."
May is able to be used with either a present or a future sense: "I am not sure whether he is there now; he may not be, but even if he is not, he may go there later." Theoretically speaking, might is the corresponding past-tense form, but since some dialects use might quite commonly with a present or future sense, it is more common to use may or might with the perfect aspect to provide a past sense: "He might have been gone when we got there, or he might have been hiding."
May is also used to express irrelevance in spite of certain or likely truth: "He may be taller than I am, but he is certainly not stronger" may mean roughly, "While it is true that he is taller than I am, that does not make a difference, as he is certainly not stronger." (However, it may also mean, "I am not sure whether he is taller than I am, but I am sure that he is not stronger.") In many dialects, might is used in this sense as well.
In addition to what has already been mentioned, might also serves as the conditional mood of may: "If he were more polite, he might be better liked." Also, while there are some dialects where the use of might to replace may is very common, even in colloquial or informal speech, there are other dialects where might serves a more polite or formal form of may, just as would does for will (see above) and could does for can (see below).
May and might do not have common negative contractions (equivalents to shan't, won't, can't, couldn't etc).
Could has at least three distinct functions. First, it can often replace can, although generally it gives the phrase a conditional tone. For example, "I can help you with your work" suggests that the speaker is ready and willing to help, whereas "I could help you with your work" gives a more tentative sense of ability to help. In this sense, could is often used like a conditional: "I could help you if you helped yourself."
Second, could functions as a kind of past tense for can, though could does not function grammatically like any regular past simple verb.
Third, could carries the same meaning as might or may in the present. That is, could suggests that something is a possibility. For instance, John is not in the office today, he could be sick. In this phrase, might or may would carry the same meaning. Note that can in the negative carries the same idea as couldn't in this sense: "He cannot have left already; why would he want to get there so early?" Also, note that when regarding potential futures actions could is not equivalent to might or may. "I might go to the mall later," does not have the same connotations as "I could go to the mall later," which suggests ability more than possibility.
In certain negative constructions, there is a different distinction between must and have to. Must not (or mustn't) indicates a prohibition ("you must not smoke in here") or a resolution not to do something ("I mustn't make that mistake again"), whereas do not have to (or don't have to) indicates that there is not an obligation either to do or to not do the verb in the sentence ("you don't have to go if you don't want to"). Nevertheless one can say "One has to not smoke", perhaps because it's prohibited or perhaps because one wants to not become unhealthy.
Both must and Have to are also used to express a strong belief that something is the case, but makes it clear that the speaker is not stating a fact but an opinion ("It must be here somewhere"). The basis of this belief is not factual but logical. In other words, we are speculating based on what we know about the world and how it works (i.e. what has happened in the past, someone's character, etc).
In standard English usage, it is rare to use more than one modal verb consecutively, with a few exceptions such as might have to or may have used to. A greater variety of double modals appear colloquially in some regional or archaic dialects. In Southern American English, for example, phrases such as might could or ought to should are sometimes used in conversation. The double modal may sometimes be redundant, as in "I ought to should do something about it", where ought to and should are synonymous and either one could be removed from the sentence. In other double modals, the two modal verbs convey different meanings, such as "I might could do something about it tomorrow", where might indicates the possibility of doing something and could indicates the ability to do it.
An example of the double modal used to could can be heard in country singer Bill Carlisle's 1951 song "Too Old to Cut the Mustard":
These kind of double modal phrases are generally not regarded as correct grammar, although other double modals may be used instead. "I might could do something about it" is more often expressed as "I might be able to do something about it", which is considered more grammatical, although in fact it is still a double modal: be able to functions here as a modal verb synonymous with could or can. Similarly used to could is usually expressed as used to be able to. Double modals can also be avoided by replacing one of the modal verbs with an appropriate adverb, such as using probably could or might possibly in place of might could.