Grammar - Can

Can
Can is an auxiliary verb, a modal auxiliary verb.

Can expresses ability. Cannot (can’t) shows inability.
She can speak four languages.
She can't dance very well.
Birds can fly.

To express a possibility (in general) - not for future possibilities. For this you would use may or might.
It can get cold there at night so take your coat.
I know you can win beat him.

To offer to do something for others
Can I help you?
Can I do that for him?

To ask for or give permission / To request something
You can borrow my bag, I don't need it right now.
Can I ask you a question?
You can't go to the zoo. It will still be wet from the rain last night.

Could is more formal and polite than can:
Could I ask a question please?
Could we go to school now?

Can't: Something that is forbidden or not allowed
You can't smoke in the school.
You cannot drive a car without a license.

Can't: when you are sure that something isn't true or something is surprising
It can't be cold outside! It's 7th of August!
They can't have landed on the March.

The negative form is can't in spoken English and cannot in written English.