Modal verbs add meaning to other verbs regarding ability, permission, obligation, possibility, and advice. "Can" expresses ability, possibility, or informal permission ("I can swim"), with "could" as its past form. "Could" also indicates polite requests ("Could you help?") or possibility ("It could rain"). "May" expresses possibility or formal permission ("May I leave early?"), while "might" indicates less certain possibility ("It might rain tomorrow").
Modals of obligation and advice range in strength. "Must" expresses strong obligation, necessity, or strong deduction ("You must wear a seatbelt," "She must be tired"). Its negative, "must not" or "mustn't," expresses prohibition and is stronger than "shouldn't." "Should" offers advice or expectation ("You should study"), while "ought to" is similar but slightly more formal ("You ought to apologize"). "Had better" ("You'd better leave now") warns of bad consequences if the advice is ignored. "Need to" expresses necessity but is more flexible than "must" because it can take various tenses, while "need not" (needn't) expresses that something is unnecessary.
Modals also express hypothetical situations. "Would" commonly expresses polite requests ("Would you help me?"), hypothetical outcomes ("I would travel if I had money"), and past habits ("When I was young, I would play in the park"). "Shall" in British English offers suggestions or formal future ("Shall we dance?"), but Americans use "will" for almost all future meanings. After modals, the base form must be used, so "She can plays" is incorrect; the correct form is "She can play."