Can

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.