Grammar - Could

Could

Could is an auxiliary verb, a modal auxiliary verb.
Could is similar to Can and often replaces Can in the past tense (though not always).

To express ability in the past
I could ride a horse when I was nine but now I can't.
He could write when he was three years old.

Polite word used to ask for permission or to request something (in the present)
Could you pass me the salt please?
Could I borrow your car?
Could you call back later?

General permission in the past
He couldn't go to the stadium because his father died.
We couldn't enter our company without employee ID card.

A suggestion when asked what to do (choices and opportunities)
He could try and fix it himself.
We could watch live footbal match on TV if you are interested.

Couldn't: Sure that something is untrue
Just like can't, you can use couldn't when you are sure that something isn't true or real.
Where are they? They could have got lost.
It's ten o'clock. They could have arrived by now.

Could + have + past participle: To express a possibility in the past
Why did you do that? You could have lost your eye.

Could + have + past participle: Unrealised past ability
She could have married anyone she wanted to.