1. Making a guess
1.1. Present situations
1.1.1. must / can't
1.1.1.1. certain that our guess is correct
1.1.2. may (not) / might (not) / could
1.1.2.1. less certain
1.1.3. may (not) / might (not)
1.1.3.1. not sure
1.2. Future situations
1.2.1. may (not) / might (not) / could
1.3. Expectations
1.3.1. should / shouldn't
1.3.1.1. expect sth to be true / feel strongly that our guess is correct
1.4. Past forms
1.4.1. Positive
1.4.1.1. might have / must have / should have
1.4.2. Negative
1.4.2.1. can't have / mightn't have / couldn't have
1.4.3. Questions
1.4.3.1. Could ... have ... Should ... have ...
1.5. Past situations
1.5.1. certain about our guess
1.5.1.1. must / can't / couldn't + have
1.5.2. less certain
1.5.2.1. may (not) / might (not) / could + have
1.5.3. not certain
1.5.3.1. mightn't have
1.6. Expectations about the past
1.6.1. should have
1.6.2. was / were supposed to
2. Rules
2.1. Positive rules and Necessary actions
2.1.1. have to
2.1.1.1. necessary things / a rule
2.1.2. must
2.1.2.1. a rule given by the speaker to themselves or another person
2.1.2.2. instructions
2.2. Negative rules
2.2.1. can't / not allowed
2.2.1.1. there is a rule
2.2.2. mustn't
2.2.2.1. explain rules and instructions
2.2.3. be allowed to
2.2.3.1. negative rules in the past and future
2.2.4. don't have to
2.2.4.1. no rule say that it's necessary
3. Necessary and unnecessary actions
3.1. necessary actions
3.1.1. need to
3.1.1.1. physically necessary things
3.1.1.2. believe sth is necessary or important
3.1.1.3. mean have to
3.2. unnecessary actions
3.2.1. needn't / don't need to, don't have to / haven't got to
3.2.1.1. sth is unnecessary or isn't a rule
3.2.2. won't need to / won't have to
3.2.2.1. unnecessary future actions
3.2.3. didn't need to / didn't have to
3.2.3.1. unnecessary things in the past
3.2.4. needn't have
3.2.4.1. an action happened in the past but wasn't necessary
4. Ability and Possibility
4.1. Future
4.1.1. be able to
4.1.1.1. used for a certain situation
4.1.2. can
4.1.2.1. used for personal arrangements
4.1.3. could
4.1.3.1. used for a posssible but unlikely situation
4.1.4. could / would be able to
4.1.4.1. used for conditional situations
4.2. Present
4.2.1. can / be able to
4.2.1.1. when sth / sb has an ability to do sth.
4.2.2. be able to
4.2.2.1. sth is surprising / requires some effort
4.2.3. can / can't + V of senses / thinking
4.2.3.1. describe an happening action
4.3. Past
4.3.1. could /couldn't was / were able to
4.3.1.1. for past ability or possibility
4.3.2. was / were able to
4.3.2.1. - making a statement about a past single event - asking a question about it
4.3.3. managed to
4.3.3.1. difficult things / with expressions like in the end, finally ...
4.4. general truths
4.4.1. can
4.4.1.1. generally possible things
4.4.2. could
4.4.2.1. generally possible things in the past