Could

'Could' is used to express: possibility, past ability, and to make suggestions and requests. 'Could' is also used in conditional sentences as the conditional form of 'can'.

Possibility You could cause an accident driving like that.
Past ability Sarah could dance like a professional at the age of six.
Suggestion We could go to dinner after the movie.
Request Could I leave early today?
Conditional If you're not working tomorrow, we could go on a picnic.

'Could' like most modal verbs, is very different in the past and future. Here are some examples of its different forms:

Possibility

Present Danny could be the team leader /Danny couldn't be the team leader
Past Danny could have been team leader / Danny couldn't have been team leader
Future Danny could be the next team leader / Danny couldn't be the next team leader

'May' or 'might' are also possible in this situation.

Suggestion

Past We could have gone to a different restaurant.
Future We could go to a different restaurant next time.

There is no present form or negative form of could used in a suggestion.

Ability

Past I could read music when I was young. I couldn't read music when I was young.

'Could' is not used in positive sentences when a momentary ability is referred to:

I was able to fix the leaky pipe myself. Not; I could fix the pipe myself
In negative sentences for a momentary ability, 'could not' is possible:
I couldn't fix the leaky pipe myself.

Requests

Could I have a coffee?
Couldn't you explain this just one more time?

'Could' is used in more polite requests.
Requests usually refer to the near future. 'Can', 'may' and might are also used for polite requests.

It is important to remember that ‘could not’ is used when it is impossible for something to happen. ‘Might not’ is used if you don’t know if something happens.

David might not have the money. Maybe David does not have the money.
David couldn’t have the money. It is not possible that David has the money.