Modal verbs
Modals (also called modal verbs, modal auxiliary verbs, modal auxiliaries) such as will, shall, may, might, can, could, must, ought to, should, would, etc. give additional information about the function of the main verb that follows it.
They have a great variety of communicative functions. They allow speakers to express ability, permission, necessity, obligation, etc. They are always followed by an infinitive without to. They never change their form (spelling). They do not need an additional auxiliary in negatives or questions (can - cannot/can't, could - could not/couldn't, may - may not, must - must not/mustn't). 
Can means capable of doing. Can is used to talk about present or general ability. (She can knit.)
Could is used to talk about ability that existed in the past. (She could write when she was three.)
May is used to ask permission (May I go out?)
Must expresses personal obligation, what the speaker thinks is necessary (He must study hard.)