Can:
- Definition: "Can" is a modal verb that is used to express ability, capability, or permission.
- Usage: It is used to talk about what someone is able or capable of doing, or to ask for permission to do something.
- Example:
- I can swim.
- Can I borrow your pen?
- She can speak five languages.

Could:
- Definition: "Could" is the past tense of "can" and is also a modal verb.
- Usage: It is used to express past ability or permission, or to make polite requests.
- Example:
- When I was younger, I could run very fast.
- Could you please pass me the salt?
- They could go to the party if they wanted to.

May:
- Definition: "May" is a modal verb used to express permission or possibility.
- Usage: It is used to ask for or give permission, or to talk about something that is possible but not certain.
- Example:
- May I use your computer?
- It may rain later, so bring an umbrella.
- She may come to the party if she finishes her work.

Comparison:
- Ability: "Can" is used to talk about present ability, while "could" is used to talk about past ability.
- She can play the piano. (She is able to play it now.)
- When I was younger, I could play the piano. (I was able to play it in the past.)
- Permission: "Can" is used to ask for and give permission in general, while "may" is used in more formal situations or to ask for permission in a polite way.
- Can I go to the park? (informal)
- May I have your attention, please? (more formal)
- Possibility: "Can" is used to talk about general possibilities, while "may" is used to talk about specific possibilities.
- It can be dangerous to swim in this river. (in general, it is possible)
- It may rain tomorrow. (specific possibility)

In summary, "can" is used for present ability and permission, "could" is used for past ability and permission, and "may" is used for permission and possibility.