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CAN, COULD, BE ABLE TO,

is an auxiliary verb, a modal auxiliary verb. We use can to

CAN

1. talk about possibility and ability

2. make requests

3. ask for or give permission

subject+auxiliary verb

can+main verb

Use of can

can for possibility and ability

We use can to talk about what is possible, what we are able or free to do:

1. She can drive a car.

John can speak Spanish.

2. I cannot hear you. (I can't hear you.)

3. Can you hear me?

COULD

Is an auxiliary verb, a modal auxiliary verb. We use could to:

talk about past possibility or ability

make requests

subject+auxiliary verb

could+main verb

Use of could​​​​​​ for past possibility or ability

We use could to talk about what was possible in the past, what we were able or free to do:

BE ABLE TO

1. I could swim when I was 5 years old.

2. My grandmother could speak seven languages.

3. When we arrived home, we could not open the door. (...couldn't open the door.)

4. Could you understand what he was saying?

Although we look at be able to here, it is not a modal verb. It is simply the verb be plus an adjective (able) followed by the infinitive. We look at be able to here because we sometimes use it instead of can and could.

We use be able to

to talk about ability

subject+be+able+to-infinitive

We use be able to to express ability. "Able" is an adjective meaning: having the power, skill or means to do something.

Be able to is possible in all tenses - but "can" is possible only in the present and "could" is possible only in the past for ability. In addition, "can" and "could" have no infinitive form.

1. I have been able to swim since I was five. (present perfect)

2. You will be able to speak perfect English very soon. (future simple)

3. I would like to be able to fly an airplane. (infinitive)