Be able to

Be able to is used to express ability to do something. (I was able to swim when I was five.) It is sometimes possible to use the modal verb can, but only in the present tense (I can speak English.), in the past tense (I could swim when I was five.) and in the conditional tense (I could try it if you helped me.).

Present tense: I am able, you are able, he is able
Past tense: I was able, you were able, he was able
Future tense: I will be able
Present perfect: I have been able, he has been able
Past perfect: I had been able
Future perfect: I will have been able

Questions and negative forms are made in the following way.
Questions: Are you able? Were you able? Has she been able?
Negative questions: Are you not able? (Aren't you able?) Has she not been able? (Hasn't she been able)?
Negative statements: I am not able, You were not able, We have not been able

Present ability

It is possible to use be able to if we talk about a general ability in the present, but can is more common.
Eve can sing very well.
Eve is able to sing very well.

Past ability

We can use was/were able to or could to talk about a general ability in the past.
Terry could speak German and French at primary school.
Terry was able to speak German and French at primary school.

But:
Could is not used to talk about a specific event (one particular action). We must use was/were able to.
Terry was able to play football on Sunday because he wasn't injured.

This rule, however, does not apply to negatives and verbs of senses or thinking. In these cases both forms are possible.
We couldn't find your address.
We weren't able to find your address.
I could hear the noise.
I was able to hear the noise.
She could understand it.
She was able to understand it.

Future ability

To talk about a future ability, we use will be able to. Can is not used for future actions.
She will be able to work next week.

Conditional ability

If we speculate about an ability in the present or future, we use either could or would be able to.
I could live in London, I think.
I would be able to live in London, I think.
Could you come tomorrow?
Would you be able to come tomorrow?

If we speculate about an ability in the past, we usually use could + perfect infinitive (could have gone), even if would have been able to is also possible.
If Terry hadn't been injured, he could have played football.
If Terry hadn't been injured, he would have been able to play football.

Other cases

In all other cases we must use be able to.
I have never been able to type.
I like being able to drive.
I'd love to be able to communicate in English.

Be able for possibility

Can is used in the present or future to express possibility.
The shop is closed. We can't go there.
The shop will be closed. We can't go there.

Could is used in the past.
You could meet her yesterday.

Be able to is used with all other tenses.
We haven't been able to go to the shop since it was closed.
We had been able to meet her before she fell ill.

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