Here's a list of the modal verbs in English:
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?').
3: They are followed directly by the infinitive of another verb (without 'to').
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'.
- 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!
AbilityWe use 'can' and 'could' to talk about a skill or ability.
- She can speak six languages.
- My grandfather could play golf very well.
- I can't drive.
Obligation and AdviceWe can use verbs such as 'must' or 'should' to say when something is necessary or unnecessary, or to give advice.
- Children must do their homework.
- We have to wear a uniform at work.
- You should stop smoking.
PermissionWe 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.
- Could I leave early today, please?
- You may not use the car tonight.
- Can we swim in the lake?
HabitsWe can use 'will' and 'would' to talk about habits or things we usually do, or did in the past.
- When I lived in Italy, we would often eat in the restaurant next to my flat.
- John will always be late!