English Subjects

MODAL VERBS

ABILITY

For an ability in the present we can use CAN or BE ABLE TO. There is no difference in meaning but CAN is more common.
-> She can play the piano

For an ability in the past we can use COULD or WAS/WERE ABLE TO. There is a difference in meaning:

(a) COULD is used for a general ability in the past
-> She could play the piano when she was six.

(b) WAS/WERE ABLE TO is used for a particular ability in the past
-> I didn't forget my keys so we were able to unlock the door.

(c) COULD can be used for a particular ability in the past when the sentence is negated, or when the lexical verb is a verb of perception
I forgot my keys so we weren't able to/couldn't unlock the door.

COULD HAVE + past participle is used to talk about an action that we had the ability to perform in the past, but that we didn't perform.
-> She could have arrived earlier.

CAN and COULD do not have non-finite forms (infinitive, -ing or participles) so they cannot we used in tenses or constructions that require those forms. Instead we have to use BE ABLE TO
-> You will be able to speak fluent Englsih in a few years.

PERMISSION

To ask for permission we may use CAN (more common, more direct), COULD (more common, less direct, more polite), MAY (more formal), or MIGHT (more formal, less direct).
-> Can she play your piano?
-> Could I use your phone?
-> May I erase the blackboard?

To give permission we may use CAN (more common, more direct),or MAY (more common, less direct, more polite)
-> Can she play your piano? Yes, she can.
-> Could I use your phone? Of course you can.
-> May I erase the blackboard? No, you can't.


To TALK ABOUT having permission we may use CAN, COULD or BE ALLOWED TO

(a) We use CAN or AM/ARE ALLOWED TO to talk about a permission we have in the present
-> The children are allowed to/can stay up late on Saturdays.

(b) We use COULD or WAS/WERE ALLOWED TO to talk about a general permission we had in the past
-> We were allowed to/could stay up late on Saturdays.

(c) To talk about a particular permission we had in the past we use WAS/WERE ALLOWED TO
-> We were allowed to stay up late last Saturday.

OBLIGATION AND NECESSITY

To express an obligation or necessity for an action in the present or the future we can use MUST or HAVE TO. There is a difference in meaning:

(a) MUST is used when the authority comes from the speaker
-> You must eat your vegetables, I insist.

(b) HAVE TO is used when the authority comes from outside the speaker
-> You have to eat your vegetables. The doctor said you need more vitamins.

MUST does not have a past tense or non-finite forms (infinitive, -ing or participles) so it cannot we used in tenses or constructions that require those forms. Instead we have to use HAVE TO.
-> Peter had to speak with his teacher after his exams.

To say that it is obligatory or necessary NOT TO DO something we use MUST NOT (MUSTN'T)
-> You mustn't eat that plant. It is poisonous.

To say that it is NOT obligatory or necessary to do something we use DON'T HAVE TO, NEEDN'T or DON'T NEED TO.
-> You don't have to eat your vegetables. Leave them if you want.
-> You don't need to come if you'd rather stay at home.

To say that something was NOT obligatory or necessary in the past we use NEEDN'T HAVE + past participle or DIDN'T NEED TO + infinitive.There is a difference in meaning.

(a) NEEDN'T HAVE indicates that something was not necessary or obligatory but that it happened anyways.
-> You needn't have come. You could have stayed at home.

(b) DIDN'T NEED TO only indicates that something was not necessary or obligatory (we do not know whether it happened or not)
-> You didn't need to come to class yesterday. Did any of you come?

POSSIBILITY, PROBABILITY, AND CERTAINTY

To that something is theoretically possible in the present or future we use CAN. For theoretical possibility in the past we use COULD.
-> Anyone can learn how to speak French.
-> My brother can be annoying. (= My bother is sometimes anoying)

To imply that something is factually possible in the present or future (that is, that perhaps something is happening or will happen) we use MAY, MIGHT or COULD. They indicate different degrees of possibility (may more likely, COULD less likely.)
-> Peter may speak with his teacher after his exams.
-> Peter might speak with his teacher after his exams.


In the negative we use MAY NOT or MIGHT NOT. In questions we rarely use MAY.
-> You may not be able to speak to him. I think he was about to leave.

To say that something is factually possible in the past (that is, that perhaps something has happened) we use MAY/MIGHT/COULD HAVE + Past participle. Tosay that something was possible in the past but did not happen we use MIGHT/ COULD + HAVE + Past participle
-> They may have arrived by now. (=Maybe they have already arrived)
-> They could have arrived by now, but they haven't.

To say that something is probable in the present or future we use SHOULD or OUGHT TO. To say that something was probable in the past we use SHOULD/ OUGHT TO + HAVE + Past participle.
-> We should be there by tomorrow morning. (=We'll probably be there tomorrow morning)
-> They ought to have arrived by now. (=Probably they have already arrived )

To say that you are sure that something will happen in the present or future we use MUST. To say that you are sure that something has happened in the past we use MUST HAVE + Past participle.
-> She must be the doctor. (=I'm sure she is the doctor)
-> They must have arrived by now. (=I'm sure they have already arrived)

To say that you are sure that something will NOT happen in the present or future we use can't. To say that you are sure that something has NOT happened in the past we use can't HAVE + Past participle.
-> She can't be the doctor. (=I'm sure she is not the doctor, it is impossible)
-> They can't have arrived by now. (=It's impossible that they have already arrived )