These modal verbs describe either something that is possible, or an action that someone is able to do.
Can is the present tense form and could is the past tense. The negative forms are cannot (can't) and could not (couldn't). Both forms are used to describe an action that is not possible.
Could have is used to describe something that was possible, but is no longer possible
We can hear the music from the park.
(We are able to hear the music.)
He could feel the cold front in the wind.
(He was able to feel the cold front...)
I can't come to the office today.
(It is not possible for me to come to the office.)
I couldn't finish the assignment.
(It wasn't possible for me to finish the assignment.)
We could have rented a convertible if we had called.