Can

Ability

We can use "can" to talk about the ability to do something in the present

Charly is in the swimming pool, is he ok?

Yes, he can swim. He completed a course with the life guards.

Equally, the negative structure is used to talk about the lack of ability:

Emily can't swim very well so you will have to watch her carefully.

Permission

We can use "can" to talk about or ask for permission

Mum, can we go to the swimming pool?

Yes, you can, but be back for dinner.

Equally, the negative form is used to talk about lack of permission or denied permission

Mum can we go to the disco with Jenny?

No, you can't, you have to finish your homework.

See also: May

Possibility

We can use "can" to talk about  the possibility of something happening

We can visit your family in August because we both have time off work then.

Equally, it can be used to talk about something we do not belive is possible:

I don't know how you can complain that you have no money, you are always buying new clothes!

Informal requests

We can use "can" to make informal requests:

It is very stuffy in here, can I open the window?

I missed the bus, can I get a lift with you?

Such requests are often made using "could" as well, but "can" is appropriate in informal contexts.

See also: Could

Offers

We use "can" as a question form to make offers:

Can I help you with that?

Making predictions or guessing (Deduction)

When we make predictions or guesses we use "can't" instead of the negative of "must" and we  use "can’t have + -ed" as the negative form of "must have + -ed". 

Is that my drink? It must be yours becuase I have not drank that much

No it can't be mine, I haven't started mine yet. 

Richard must have made alot of money

He can't have done, he still drives that old rusty car.

"Can’t" and "can’t have + -ed" both express strong possibility:

She can't be single, she is so beautiful.  

You can't have finished your homework, you have only been in there for forty minutes.

See also: Could, Must

General Truths

We sometimes use "can" to talk about things that are generally or often true. Such things are not always true in all circumstances. 

It can get very hot in the summer

It can be very difficult to get a job in television

This use is often very similar to expressing possibility

Learning Spanish can be very difficult

(It might not be difficult for everyone)

You can sometimes find a parking space in our street

(It is possible but not certain)

See also: Could

Admonishment

We often use can't in a question form to ask someone to stop doing something we do not approve of. 

Can't you just go out with your friends and not get drunk?

Can't you be pleasent while my parents are visiting?