Useful table about Modal Verbs

What I want to say	How I say it	What I actually say
-talk about your abilities	can could be able to	I can speak English. I could swim when I was 6. I was able to climb the top of the mountain.
-talk about the lack of abilities	can't couldn't not be able to	I can't speak English. I couldn't swim when I was 6. I wasn't able to climb the top of the mountain.
-ask for permission	informal: can more polite: could formal: may/might	Can/Could/May I ask you a question?
-give permission	informal: can polite: may formal: be allowed to	You can park your car here. You may park your car here. You're allowed to park your car here
-refuse permission	informal: can't polite: may not/mustn't formal: not allowed to	You can't park your car here. You mustn't park your car here. You're not allowed to park your car here
-make request	informal: can/will more polite: could/would formal: may/might	Can/Could I have some water?(it hasn't meaning of a question!) Can/Will/Could/Would you explain that to me? May I have some water?
-offer smth	shall can could	Shall we dance? We can/could go to the theatre today.
-give advice	should ought to must	You should/ought to/must study harder.
-critisize the person	should (+not , if negative) ought to + have + verb in third form	You should/ought to have listened to me.
-tell everybody what is necessary to do	must have to need	You must study English better. I have to wake up early tomorow. Need I buy her a present?.
-tell everybody what isn't necessary to do	don't need to don't have to needn't	You don't have to go shopping, I'll do it.
-it wasn't necessary and you didn't do it	didn't need to didn't have to	I didn't have to go shopping yesterday, because my boy friend had already done it.
-it wasn't necessary but you did it	needn't + have + verb in third form	I needn't have done the shopping. (but i did it)
-want to say that you are sure	must(positive) / can't(negative) +1)verb +2)be+ verb+ing +3)have+verb in third +4)have been + Verb+ing	I am sure 1)she is a doctor. 2)she is sleeping now. 3)she bought a car. 4)she was cooking when he was killed. She must 1)be a doctor. 2)be sleeping now. 3)have bought a car. 4)have been cooking when he was killed.
-want to say that smth is possible	might may could	1)Perhaps they love each other. 2)It's possible that they're having coffee now. 3)Perhaps they kissed. 4)It's likely they have been hiding. 1)They may love each other. 2)They could be having a coffee now. 3)They might have kisses. 4)They may have been hiding.