Here's a list of the modal verbs in English:
can could may might
must shall should ought to
Modals are different from normal verbs:
1: They don't use an 's' for the third person singular.
2: They make questions by inversion ('she can go' becomes 'can she go?') instead of using the auxiliar.
3: They are followed directly by the infinitive of another verb (without 'to').
Probability
First, they can be used when we want to say how sure we are that something happened/is happening/will happen. We often call these 'modals of deduction' or 'speculation' or 'certainty' or 'probability'.
For example:
It's snowing, so it must be very cold outside.
I don't know where John is. He could have missed the train.
This bill can't be right. £200 for two cups of coffee!
Ability
We use 'can' and 'could' to talk about a skill or ability.
For example:
She can speak six languages.
My grandfather could play golf very well.
I can't drive.
Obligation and Advice
We can use verbs such as 'must' or 'should' to say when something is necessary or unnecessary, or to give advice.
For example:
Children must do their homework.
We have to wear a uniform at work.
You should stop smoking.
Permission
We can use verbs such as 'can', 'could' and 'may' to ask for and give permission. We also use modal verbs to say something is not allowed.
For example:
Could I leave early today, please?
You may not use the car tonight.
Can we swim in the lake?
Now, about the
Perfect Modals...
Could have/couldn’t haveThis denotes past ability, how you had this option in the past but now the choice no longer exists.
For example:
I could have gone to Africa when I was 16.
You could have been a rockstar, you were really good at playing the guitar.
Should have/shouldn’t have
These denote past obligation, something that you had to do in the past for the result to be favourable now. Something that was desirable, but did not happen.
For example:
He should have gone to the bank earlier, he knew he had to pay the bill today.
She shouldn’t have touched their property, that wasn’t the right thing to do.
May have/may not have/ might have/might not have.
These constructions denote past possibility, they usually describe something about which you are not quite certain.
For example:
I may have left it at home, but I’m not sure.
We might go to the party later, if you want to come.
Must have/must not have
This denotes past probability, something of which you are nearly certain but of which you are not quite sure.
For example:
I must have been really drunk last night because I don’t remember much!
She must not have heard me properly because I didn’t say that.
And, since practice makes perfect, here you have some exercises to do: