Modals - Could X Couldn´t - possibility, ability 

'Could' can be used to talk about the past, the present or the future.

'Could' is a past form of 'can'

• When I was living in Boston, I could walk to work.

• He phoned to say he couldn't come.

• I could see him clearly but I couldn't hear him and then the videoconference line went dead.

'Could' is used to make polite requests. We can also use 'can' for these but 'could' is more polite.

• Could you help me, please?

• Could you lend me some money?

• Could I have a lift?

• Could I bother you for a moment?

If we use 'could' in reply to these requests, it suggests that we do not really want to do it. If you agree to the request, it is better to say 'can'

• Of course I can.

• I could help you if it's really necessary but I'm really busy right now.

• I could lend you some money but I'd need it back tomorrow without fail.

• I could give you a lift as far as Birmingham.

'Could' is used to talk about theoretical possibility and is similar in meaning to 'might'.

• It could rain later. Take an umbrella.

• He could be there by now.

• Could he be any happier?

• It could be Sarah's.