We use 'can' to talk about 'possibility'.
- 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.