The verb CAN is most often used to talk about permission and ability.

Welcome to twominuteenglish.com. Teaching you English in two minutes or less. In this lesson we will tell you how to seek permission to do something, and also to tell someone whether you can or can’t do something.

Hey Susan, Ben just called, he asked me to hang out with him.
But John! It’s almost Christmas you have to put up the decorations.
I can always do that later. Can’t I?
John! You can hang out with your friends later too.
You are telling me I can’t go out?
I am saying you shouldn’t.
Alright dear. I will call him up and tell him I can’t come.

Are you sure this is a good idea? We can always order something.
Of course it is! I’ve planned everything. I can make us dinner today.
If you are so certain you can cook, why do I smell smoke?
Oh, no! I can’t believe I forgot to turn off the oven!

Would you mind telling me about your computer skills, Mr. Harper?
I am an expert with MS Word and Excel and I can manage databases on Access.
Okay, very good. And could you travel on business?
Absolutely! Yes.
How soon can you start?
As soon as you need me to, Ma’am!

When I was younger, I couldn’t travel abroad because I didn’t have the money and I couldn’t speak English.
But you currently have a job that pays you well and you can also speak English now.
So you should travel now.
Well...I can afford to travel but I can’t do it because I don’t have the time!
If you really want to travel, you can find a way.
You’re right, I can and I should.

Could I talk to you for a minute, Ms. Smith?
Yes, what is it, John?
Could I take my test next week? I feel I am not ready to take it tomorrow.
I’m afraid you should talk to the coordinator about this.
Okay, I will.

REPEAT

I can always do that later. Can’t I?
Oh, no! I Can’t believe I forget to turn off the oven!
Oh, no! I Can’t believe I forget to turn off the oven!
When I was younger, I couldn’t travel abroad.
I can afford to travel but I can’t do it because I don’t have the time!

One of the most common uses of CAN is to ask for permission or to deny permission.

- Can I go out with my friends tonight? - No, you can't, we have to visit my parents. But you can go for a quick drink and be back before 7.

Also, we often use CAN to talk about abilities.

- I can speak English very well, but I can't speak French

COULD may be the past tense or the conditional form of CAN.

- When I was a child, I could run faster than any of my friends
- If you helped me, we could finish this in a minute.

We also use COULD as a more polite form of CAN:

- Can you help me with this? --- Could you help me with this?