Chris presents some ideas about different ways to use can, could and to be able to. Via YouTube

CAN = modal verb

I can do it or I can’t (cannot) do it

can’t use it in the past

can for permission: Can I go out? You can’t smoke here (instruction)

can for ability: I can speak three languages or I can’t speak three languages

can in the future: I can see you tomorrow

COULD = can in the past  (modal verb)

I could come or I couldn’t (could not) come (past)

could for questions (more polite):

Could you do that outside, please?

could = can in the past: I could do that when I was younger

couldn’t for something you don’t want to do:

I couldn’t make fun of him (it is possible but I don’t want to)

TO BE ABLE TO is possible with the past and future – not a modal verb

able – ability (noun)

I’m able to see him now or I’m not able to see him now

use with future + will:

I will be able to come tomorrow

I won’t be able to come tomorrow

use to be able to in the past:

I was able to do that when I was younger

I used to be able to do that

‘can’ is more common than ‘be able to’ because it’s shorter and more useful