•Can you do that?
•I can't manage to do that.
•You can leave your car in that parking space.
•You cannot smoke in here.
Notice that there are two negative forms: 'can't' and 'cannot'. These mean exactly the same thing. When we are speaking, we usually say 'can't'.
We use 'can' to talk about 'ability'.
•I can speak French.
•I can't drive.
We use 'can' to ask for and give permission. (We also use 'may' for this but is more formal and much less common.)
•Can I speak to you or are you too busy?
•You can use my phone.
•You can't come in.
We use 'can' in offers, requests and instructions.
•Can I help?
•Can you give me a hand?
•When you finish that, you can take out the garbage.
We use 'can' with 'see' 'hear' 'feel' 'smell' 'taste' to talk about something which is happening now . (Where you would use the present continuous with most other verbs.)
•I can smell something burning.
•Can you hear that noise?
•I can't see anything.
We can use 'can't' for deduction. The opposite of 'can't' in this context is 'must'.
•You can't be hungry. You've just eaten.
•You must be hungry. You haven't eaten anything all day.
•He was in London one hour ago when I spoke to him. He can't be here yet.