1. Definition
1.1. Modal verbs are auxiliary verbs that express a necessity or possibility.
2. The modal verbs are:
2.1. could
2.1.1. Asking for permission
2.1.1.1. Could I borrow your dictionary
2.1.2. Request
2.1.2.1. Could you say that again more slowly?
2.1.3. Suggestion
2.1.3.1. We could try to fix it ourselves
2.1.4. Future possibility
2.1.4.1. I think we could have another problem
2.1.5. Ability in the past
2.1.5.1. He gave up his old job so he could work for us
2.2. Can
2.2.1. Ability/Possibility
2.2.1.1. They can control their own budgets
2.2.2. Inhability/Impossibility
2.2.2.1. We can't fix it
2.2.3. Asking for permission
2.2.3.1. Can I open the door?
2.2.4. Request
2.2.4.1. Can you help me?
2.3. may/might
2.3.1. Formal Permission / Formal Prohibition
2.3.1.1. You may start your exam now.
2.3.2. Possibility / Negative Possibility
2.3.2.1. may/ might + base form of the verb
2.3.2.1.1. Our company might get the order if the client agrees to the price.
2.4. will
2.4.1. will / won’t + base form of the verb
2.4.1.1. Example: Ana will take you to de doctor.
2.4.2. Polite request or statement
2.4.2.1. Will / Would + base form of the verb
2.5. shall
2.5.1. To offer help or giving a polite suggestion.
2.5.2. Shall + subject + base form of the verb
2.5.3. Example: Shall we go shopping?
2.6. should
2.6.1. Example: The proposal should be finished on time.
2.6.2. In prediction or expectation that something will happen and to give advice.
2.6.3. should/shouldn't + base form of the verb
2.7. ought to
2.7.1. To give advice
2.7.2. Ought to + base form of the verb
2.8. must /have to
2.8.1. Necessity or Requirement
2.8.1.1. I had to work late last night.
2.8.2. Prohibited or Forbidden
2.8.2.1. You mustn’t leave medicines where children can get to them.
2.8.3. To Persuade
2.8.3.1. You have to visit us while you’re in town.
2.9. would
2.9.1. Asking for permission
2.9.1.1. Would you mind if I bring my cousin?
2.9.2. Request
2.9.2.1. Would you pass the salt?
2.9.3. Making arragenment
2.9.3.1. "Would three o'clock suit you?" - "That'd be fine"
2.9.4. Invitation
2.9.4.1. Would you like to play golf this Friday?
2.9.5. Preferences
2.9.5.1. "Would you prefer tea of coffee" - "I'd like tea, please"