Present:

• «Can», «cannot» or «am/is/are able to» are used for ability, skill or knowledge.

• Many disabled people can't walk. = Many disabled people are not able to walk.
• Most babies can walk when they are one year old (they know how to do it).
• I can speak three languages.
• Can you open this window? (= Are you strong enough to open it?)

Past:

• «Could», «could not» or «was/were able to» are used for ability.

• Could you talk to your boss yesterday?
• I couldn't open this window yesterday (because it was stuck).
• Sorry, I wasn't able to fix the toaster.

Hypotheses:

• «Could», «could not» or «would be able to» are used for the conditional.

• I couldn't eat all that food. = I would not be able to eat such a big amount of food.

Future, etc.

• «Will be able to», «have been able to», etc. are used in all other tenses.

• You won't been able to read the document (because the file is corrupted).
• I hadn't been able to contact him all day.
• Will you be able to finish this by tomorrow?

Present:

• «Can» is used to express that it is possible or feasible to do something. This use is very similar to ability, but it does not refer to a person's ability to do something, but to whether it is possible or impossible to do it.
• «Cannot» is used to express that something is impossible or unfeasible.

• You can ski in Spain in the winter (= It is possible to do it, because there are high mountains.)
• You can't ski in Spain in the summer. (= It is impossible because there is no snow.)
• We can't open this window (because it is the kind that does not open).

Past:

• «Could not» is used to express that something was impossible.
• «Cannot have» and «could not have» are used to express that it is impossible that something has happened (see also certainty / deduction).

• We couldn't ski because the snow was melting, so we went for a walk instead.
• We couldn't open the window, so we brought a fan. (= It wasn't the sort of window that can be opened.)
• He can't have arrived in New York yet.
• He couldn't have cheated in the exam, he's a brilliant student.

Present:

• «May», «might» and «could» express probability (meaning something is possible, probable or likely) in the present.
• «May not» and «might not» mean it is not probable or likely (but «could not» means it was impossible).

• The window may be open. (= It is possible it is open.)
• The library might be open until five. (= I am not sure.)
• The supermarket could be open all day. (= It is likely we can buy what we need there.)
• The bookshop may not be open at this time.
• The bookshop might not open on Saturday evening.

Past:

• «May have» and «might have» mean that it is probable or likely that something has happened.
• «Could have» expresses possibility (meaning it was possible or likely) in the past.
• «Could have» is used to express that something was possible or likely.
• «May not have» and «might not have» can express possibility, but «could not have» expresses impossibility only.

• The window may have been open. (= It is possible that it was open, or I think it was open.)
• The window might have been open.
• Driving and sending a text message? Are you crazy? You could have had an accident!
• He may or may not have stolen it (= maybe he has, maybe he hasn't).

Present:

• «Must» and «have to» express certainty.
• «Cannot» and «could not» express negative certainty.
  

• The window must be open. (= I am sure it is open, because it is cold in here.)
• The window has to be open. (= I am sure it is the only explanation for the cold in here.)
• The window can't be open. (= I am sure it is closed.)
• That woman couldn't be her daughter. (= I am sure the woman I saw with her is her sister.)

Past:

• «Had do» expresses certainty in the past.
  
• «Must have», «cannot have» and «could not have» are used for deduction about past events.

• The window had to be open. (= I am/was sure it was the only explanation.)
• He must have been late. (= I am sure he was late.)
• They can't have bought a new car. (= I am sure they don't have enough money.)
• They couldn't have said that. (= I am sure they didn't say that.)

Present:

• «Will» and «should» can express a supposition or assumption in the present.
  
• «Will» expresses more certainty than «should».
• «Ought to» is also possible, but not as common as «should».

• The heating will be off. (= I think it is probable that heating is off, because it is cold in here).
• Mr. Brown should be at his office. (= I think it is probable that he is there, because he is usually punctual).

Future:

• «Will» and «should» can also express a supposition or assumption in the future.
  

• Your teacher will (probably) tell you what you have to study for the exam. (= I assume she will very probably do that).
• Your teacher should tell you what you have to study for the exam. (= I suppose she will probably do that).

Past:

• «Will have» expresses a supposition or assumption in the past.
• «Should have» is not so common.

• They will have sent an e-mail to all the team members. (= I'm fairly sure they are all informed, because they always do that.)
• He took his driving test yesterday. He should have passed it, but I haven't been able to ask him yet.

Present:

• «Must» and «have to» express obligation.
• «Should» and «ought to» can express obligation, too, when the context makes it clear.
• «Must» expresses the speaker's authority, «have to» expresses an external authority (but «must» is never used in the past, so «had to» can express both types of authority).
• «Must not» expresses prohibition.
• «You shall» expresses very formal obligation.
• «You shall not» expresses very formal prohibition.
• «Should not» and «ought not to» can also express a prohibition.
• «Do/does not have to», «do/does not need to» or «need not» express absence of obligation in the present.

• You must / have to / should / ought to open the window (if you smell gas).
• You mustn't smoke in here (because it is very dangerous).
• You shall do as you are told, young man.
• You shall not talk to those people again, do I make myself clear?
• You shouldn't / oughtn't to smoke in here. (= I think it is forbidden)
• You don't have to / need not / don't need to open the window (but you can, if you like).

Past:

• «Had to», «should have» and «ought to have» express obligation in the past.
• «Did not have to», «did not need to» express absence of obligation in the past.

• You must / have to / should / ought to open the window (if you smell gas).
• I had to open the window (because I could smell gas).
• You mustn't open the window (because it is cold).
• You don't have to / need not / don't need to open the window (but you can, if you like).
• He didn't have to / didn't need to open the window (so he probably didn't).
• You needn't have opened the window (but you did).

• «Must not» is used especially when the speaker has the authority to enforce the prohibition.
• «Cannot» is more colloquial.
• «May not» is more formal and impersonal; it is often used in signs.

• Please remember you must not run in the corridors.
• We cannot smoke in here.
• Customers under 18 may not order alcoholic drinks.

Present:

• «Can», «could», «may», «might» and «am/is/are allowed to» are used to ask permission.
• «Could» is the most frequent.
• «Can» is the most colloquial.
• «May» is more formal.
• «Might» expresses more uncertainty.
• «May (not)» and «cannot» are used to grant or deny permission.

• Can I borrow your rubber, please?
• Could you lend me your calculator, please?
• May I go to the toilet, please?
• Might I open the window, if you don't mind?
• May we use a dictionary? No, you are not allowed to (do that).
• No, you may not (use a dictionary).
• Yes, you may (open the window).
• Yes, of course you can, go ahead.
• No, I'm afraid you can't, sorry.

Past:

• «Could» and «was/were allowed to» are used for permission.

Examples:

• Could you open the window? (or didn't they let you do it?)
• Were you allowed to open the window?

• «Need» is a semiauxiliary verb: the negative form may be «need not» or «don't/doesn't need to».
• In the past it can be used in two different ways: «I didn't need to» (= No tuve que...) implies that I did not do it because it was not necessary; «you need not have + V-en» (= No hacía falta que...) implies that you did it, but you shouldn't have bothered.
• «Not have to» is the same as «needn't». It is important not to confuse it with «mustn't» (see prohibition).

• You needn't decide now. / You don't need to decide now.
• You don't have to come with me if you have other things to do.
• That's very kind of you, but you needn't have gone to so much trouble.
• We didn't need to buy tickets because we had been invited to the backstage.

• «Should» and «ought to» are used to give or ask for advice.
• «Wh-word + should I/we» are used to ask for advice.
• «had better is used to give strong advice or a warning.

---

• «Must» and «have to» can be used to express emphatic advice.

• You should open the window (it is a bit hot in here).
• You ought to see a doctor if your back aches so much.
• Should I buy a new toaster, do you think?
• Ought I to schedule another meeting?
• What clothes should I bring to the trip?
• What time should we start making the sandwiches?

---

• You must see Harrison Ford's new film, it is fantastic.
• You have to try this, it's delicious!

• «Can» and «could», often followed by "always", can be used to make a suggestion.
• «Will» is used to make an offer.
• «Wh-word + shall I» is used to ask for instructions.
• «Wh-word + shall we» is used to ask for suggestions.
• «Shall I» is used to make an offer.
• «Shall we» is used to make a suggestion.
• «(Wh-) + shall + I / we + V» can be translated as the present simple in Spanish.

• You can use a pencil rather than a pen, in case you make a mistake.
• I will help you with that suitcase.
• We could always eat a pizza at home if you think a restaurant would be too expensive.
• How many tickets shall I buy?
• What shall we do on Saturday?
• Shall I post this letter for you?
• Shall we go to the cinema this evening?

• «Should have», «could have» and «might have» are used to express reproach.
• «Should have» can sound quite friendly, but «could have» and «might have» express a complaint.
• «Should not have» is the only one that can be used in the negative.

Examples:

• You should have opened the window if you were hot.
• You could have / might have opened the window! It's really hot and stuffy in here!
• You shouldn't have opened the window, look at all these flies.

• «Can you», «could you», «will you» and «would you» are used to ask someone to do something.
• «Can you» is the most colloquial one.
• «Could you» is more polite, so it is the most common.
• «Will you» is the least polite one, it can be quite insistent.
• «Would you» is the most formal one.
• «Can I» can be used for a familiar request. It is a similar function to that of asking for permission.
• «May I» can be used for a formal request.
• «Might I» can be used for a very formal and polite request.
• To ask for a thing you can also use «can I have», «could I have», «may I have» and «might I have».
• Be careful: if used in the negative, they can be very insistent, or even express a reprimand, especially «can't».
• Very often they are used as question tags after an imperative sentence, to modify its pragmatic meaning, for example to soften a command or to make a request more insistent.

• Can you hang on a second, please?
• Could you wait here a moment, please?
• Will you stop talking, please?
• Would you (be so kind as to) tell him to phone me, please?
• Can I have a tuna and tomato sandwich, please? How much is it?
• Could I have some more cake, please?
• May I see your driver's licence, sir?
• Can I come to the cinema with you, please?
• Might I have the window seat, if you don't mind? I tend to get carsick easily, you see.

• «Would you (like to)» and «will you» are used to invite someone to do something, or have something to eat or drink.
• «Won't you» is used for a more formal invitation.

• Would you like to sit by the window?
• Would you try this cake? I baked it this morning.
• Will you have a cup of tea?
• Won't you have another biscuit?

• «Used to» and «would» are used to describe past habits which are not maintained in the present, or routines in the past which may or may not be kept in the present.
• «Used to» can also describe past states which are not the same in the present.

• I used to play after school with my friends for half an hour before we went home.
• We would play near an old tower.
• They used to live in that house before they moved to London.

• «May as well» and «might as well» are used to give a piece of advice when we think that it will make little or no difference.
• It is used especially when we think there is no better choice, or no other option:
  
• If you add "just", it sounds more like a piece of advice than a suggestion:
  

Examples:

• You might just as well throw it away, no one's going to want it.
• I'm sure no one else is going to come. We may as well stop waiting and leave now.
• This film is really boring. I might as well turn off the TV.