What’s the difference between CAN, COULD, and ABLE TO?

In the present:

“Can” and “able to” are the same in the present tense:

Yes, I can take on this project.

Yes, I‘m able to take on this project.

The negative forms are can’t and am not / is not / are not able to.

In the past:

We use “could/couldn’t” or “was/wasn’t able to.”

In general, both are used in the negative form:

I wasn’t able to finish all my homework yesterday.

I couldn’t finish all my homework yesterday.

But in the positive form, “was able to” is more common than “could”:

I was able to leave work a little early yesterday.

Don’t say didn’t can in the past – it doesn’t exist, and it’s a common error in English!

In the future:

In the future, there is only one form: “will be able to”:

I have some free time tomorrow, so I‘ll be able to work on this project.

Sorry, I won’t be able to go to the party on Thursday. I have school the next day.

Don’t say “will can” or “won’t can” - it’s another common error in English!

When asking someone to do something:

When you are asking someone to do something, use “could” (more formal) or “can” (more informal):

Could you bring me a glass of water, please?

Can you bring me a glass of water, please?

When asking about someone’s abilities:

In this case, you can use either CAN or ABLE TO:

Can you run a mile in less than 10 minutes?

Are you able to run a mile in less than 10 minutes?

Can is probably more common in spoken English, simply because it’s shorter.

Source: http://www.espressoenglish.net