1. Ability
1.1. Can
1.1.1. Expressing ability now or general
1.1.1.1. I can run a kilometre in four minutes.
1.1.2. Expressing decisions made now about future ability
1.1.2.1. We can mett at the gym tomorrow, if you like.
1.2. Could
1.2.1. Expresing ability at the past
1.2.1.1. I could do fifty press-ups with one hand when i was younger.
1.2.2. Expressing ability at the present, future or general hypothetical situations
1.2.2.1. If only I could quit smoking.
1.3. Could + perfect infinitive
1.3.1. I could have roasted the potatoes, but i decided that boiling them was healthier.
2. Permission
2.1. May/ould/can
2.1.1. Asking for and giving permission now, for the future or generaly
2.1.1.1. May/could/can I see the doctor, please.
3. Advice
3.1. should/ought to
3.1.1. Asking for and giving advice now,for the future or generally
3.1.1.1. You ought to/should cut down on the amount of red meat you eat.
4. Criticism
4.1. should/ought to (+ perfect infinitive)
4.1.1. Criticism past behaviour
4.1.1.1. He uoght to/should have made to more of an effort with his diet.
5. Obligation and necesity
5.1. must/have to/need to
5.1.1. expressing obliagtion or necessity
5.1.1.1. I must/have to/need to pick up that prescription from the chemist on the way home
5.2. Needn't/don't have to/don't need to
5.2.1. Expressing lack of obligation on necessity
5.2.1.1. You needn't/don't have to/don/t need to pick up that prescriptions from the chemist as i'll get it while i'm in town
5.3. had to
5.3.1. Expressing past obligation
5.3.1.1. I had to take the pills three times a day for two weeks
5.4. needn't(+ perfect infinitive)/didn't have to/didn't need to
5.4.1. Expressing lack of past obligation
5.4.1.1. I needn't have gone/didn't have to/didn't need to go to the doctor
6. Degrees of certainty
6.1. must/can/couldn't
6.1.1. Expressing certainty (or near certainty) about now or generally
6.1.1.1. That must be the district nurse at the door.
6.1.1.2. These can't/couldn't be the pills; they're the wrong color
6.2. must/can't/couldn't(+ perfect infinitive)
6.2.1. Exprassing certainty (or near certainly) about the past
6.2.1.1. She must have been in a lot of pain.
6.2.1.2. His leg can't/couldn't have been in plaster for two years.
6.3. should/ought to
6.3.1. Expressing probility about now, the future or generally
6.3.1.1. You ought to/should feel better ni a few days, as long as you get losts of rest.
6.4. should/aught to(+ perfect infinitice)
6.4.1. Expressing probility about the past
6.4.1.1. The bruise ought to/should have dissapeared days ago. I wonder why it didn't.
6.5. could/may/might
6.5.1. Expressing possibility about now, the future or generally
6.5.1.1. You should talk to your doctor first because that diet could/may/might be dangerous.
6.6. coulg/may/might(+ perfect infinitive)
6.6.1. Expressing possibility about the real past
6.6.1.1. That could/may/ might have been the doctor reng earlier while we were out.
6.7. could/might(+ perfect infinitive)
6.7.1. Expressing possobility about a hypothetical past
6.7.1.1. It's a good thing you went to the doctor or you could/might have become quite ill.