Both can and may can be used to talk about possibility. But there is some difference between them. Can is used to talk about theoretical possibility; may is used to talk about factual possibility.

Compare:

• The road may be blocked due to the procession. (Factual possibility.)
  
• Any road can be blocked. (Theoretical possibility - It is possible to block any road.)
  
• There may be a strike next week. (It is possible that there will be a strike next week.)
  
• Strikes can happen any time. (It is possible for strikes to happen any time.)
  
• If you drive carelessly, you may have an accident. (Factual possibility)
  
• Accidents can happen any time. (Theoretical possibility)
  

When we talk about possibility, could often means the same as may or might.

• You may/might/could be right.
  

May not and Cannot

May not suggests improbability. Cannot suggests impossibility.

Compare:

• We may not go camping this summer. (= It is possible that we may not go camping.)
  
• We cannot go camping this summer. (= It is not possible for us to go camping this summer.)

May is a modal auxiliary verb. There is no –s in the third person singular.

• She may be here soon. (NOT She mays …)

May is followed by an infinitive without to.

• You may be right. (NOT You may to be right.)
• He may come.

Questions and negatives are made without do.

• May I come in, please? (NOT Do I may come …)
• He may not come. (NOT He do not may come.)

May does not have infinitives (to may) or participles (maying, mayed). When necessary, we use other words.

Meaning

May is used to talk about possibility, and to ask for and give permission.

• It may rain this afternoon.
• May I play carroms, mummy?
• Yes, you may.

Possibility

May is used to talk about the chances of something happening.

• I think it is going to rain. You may be right.
• There may be a strike next week.
• Where is John? He may be out shopping.

May well is used to suggest a strong possibility.

• I think it is going to rain. You may well be right.

May is not normally used in direct questions about probability.

• Are they likely to help us? (BUT NOT May they help us?)

But note that may is possible in indirect questions about probability.

• May we not be making a big mistake?

May + perfect infinitive

The structure may + perfect Infinitive (have + past participle) can be used to say that it is possible that something happened or was true in the past.

• Alice is very late. She may have missed her train. (= It is possible that she missed her train.)

May + perfect infinitive can also refer to the present or future.

• I will try phoning him, but he may have gone out by now.

Permission

May can be used to ask for permission. It is more formal than can and could.

• May I come in?

May is used to give permission; may not is used to refuse permission and to forbid.

• May I come in? Yes, you may.
• May I have a look at your papers? No, I am afraid you may not.

Must not is also used to forbid. It is stronger than may not.

• Students must not use the staff car park.

May and might are not normally used to talk about permission which has already been given or refused, about freedom which people already have, or about rules and laws. Instead, we use can, could or be allowed.

• Can you/Are you allowed to park on both sides of the road here? (More natural than May you allowed …)
• When we were children, we could watch TV whenever we wanted to. (NOT …we might watch TV …)

May in wishes and hopes

May is used in formal expressions of wishes and hopes. May often comes at the beginning of the sentence.

• May God bless you!
• May you both be very happy!
• May the devil take him!
• May you prosper in all that you do!

Could is an auxiliary verb, a modal auxiliary verb. We use could to:

• talk about past possibility or ability
• make requests

Structure of Could

subject + could + main verb

The main verb is always the bare infinitive (infinitive without "to").

Notice that:

• Could is invariable. There is only one form of could.
• The main verb is always the bare infinitive.

Uses

To talk about past ability in general

Could is often used to say that somebody was able to do something in the past.

• My father could walk without help when he was 95.
  
• She could read when she was 3.
  
• When we were children, we could watch TV whenever we wanted to.
  
• In my younger days, I could run four miles at a stretch.
  

Note that could refers to the past only when the context makes the time clear.

Could not (also couldn't) shows past inability.

• I could not understand a word, but I kept smiling.
  
• She spoke in such a low voice that most of us could not hear her.
  
• We found that we couldn't depend on our guide.
  

Could is used to talk about past ability in general. We do not normally use could to say that somebody managed to do something on one occasion. But with certain verbs like see, hear, taste, feel, smell, understand, remember etc., could can be used for particular occasions as well.

• Suddenly I could hear a loud noise.
  
• I could smell something burning.
  

As the past equivalent of can

Could is the past equivalent of can in indirect speech.

• He said, "I can drive."
  
• He said that he could drive.
  
• She said, "I can't climb up the hill."
  
• She said that she could not climb up the hill.
  

To make polite requests or offers

Could is often used to make a request or offer sound more polite.

• Could I have a glass of water, please?
  
• Could you help me with these bags?
  

To express possibility or uncertainty

Could can mean would be able to.

• You could get a better job if you spoke English. (=You would be able to get a better job if you spoke English.)
  
• You could do it if you tried hard. (=You would be able to do it…)
  
• If only I had some working capital, I could start a new business. (=…I would be able to start a new business.)
  

Could have + past participle

The structure could have + past participle can be used to criticize people for not doing things. It can also be used to talk about past events that did not happen.

• I have been waiting since morning - you could have said that you weren't coming.
  
• Why did you drive so carelessly? You could have killed yourself.

Can is an auxiliary verb, a modal auxiliary verb. We use can to:

• talk about possibility and ability
• make requests
• ask for or give permission

Structure of Can

subject + can + main verb

The main verb is always the bare infinitive (infinitive without "to").

Notice that:

• Can is invariable. There is only one form of can.
• The main verb is always the bare infinitive.

Uses

Can is used to talk about ability and possibility, to ask for and give permission, and to make requests and offers.

To talk about theoretical possibility

We can use can to talk about ‘theoretical’ possibility – to say that situations and events are possible theoretically.

• Glass can be blown. (It is theoretically possible to blow glass.)
  
• Wars can break out any time. (It is theoretically possible for wars to break out any time.)
  
• Smoking can cause cancer.
  
• Noise can be quite a problem when you are living in a city.
  

Note that we do not use can to talk about future probability – to say that something will happen in future. We express this idea with may or might.

• It may rain this evening. (NOT It can rain …)
• There may be a strike next week. (NOT There can be a strike …)
• I may get a job soon.

Note that might expresses a less definite possibility than may. Could is also used in the same sense.

• It could rain this evening. (= It might rain this evening.)

To talk about logical possibility

Can is often used in questions and negatives to talk about the logical possibility that something is true.

• There is the doorbell? Who can it be?

With this meaning can is not possible in affirmative clauses. Instead, we use could, may or might.

• Where is John? He could/may/might be in the garden. (NOT He can be in the garden.)

To talk about ability

We can use can to talk about present or general ability – to say that we are capable of doing something.

• I can speak 10 languages.
  
• She can cook well.
  
• Can you knit?
  
• If you are not satisfied with this product, you can send it back.
  

Note that be able to can often be used with similar meanings.

• He is able to support her. (= He can support her.)
• They were able to catch the thief. (= They could catch the thief.)

Cannot (also can’t) shows inability.

• I can speak French, but I cannot write it.
  
• Most people cannot read traffic signals.
  
• I can't drive.
  

We do not use can to talk about future ability. Instead, we use will be able to or other words.

• Someday scientists will be able to find a cure for cancer. (NOT Someday scientists will can find a cure for cancer.)
  

To ask for or give permission

Can is sometimes used to ask for and give permission. Some people, however, think that maycan. is more correct than

• Can I use your car, John?
  
• Can we park over there?
  
• You can go out and play after you have finished your homework.
  
• You can park on either side of the road here.
  
• Can I go to the movies, mom?
  

Note that we can also use could to ask for permission. It is a more polite form of can .

• Could I speak to Mr. John, please?
  
• Could I have look at your newspaper?
  

Cannot is used to refuse permission.

• Can I go to the movies, mom? No, you can’t.

To make requests and offers

Can is used in polite requests and offers of help.

• Can you turn that music down? I am trying to work.
  
• Can you get me a cup of coffee?
  
• Can I help you with those bags?
  

Note that Could is a more polite way of making requests and offers.

• Could you help me with my homework?
  
• Could you lend me some money?

An auxiliary verb is one which helps other verbs to make tenses, passive forms etc. There are two groups - primary auxiliaries and modal auxiliaries.

Modal auxiliaries

The verbs will, would, shall, should, can, could, may, might, must, ought, dare and need are usually called modal auxiliaries. They are used with other verbs to express actions, events or situations that exist only as conceptions of the mind - permissions, possibilities, certainty, ability, wishes, obligations etc. They may also express simple futurity.

• I can swim.
  
• She will come.
  
• I must go now.
  
• Should I call them?
  
• She might come.
  

Modal auxiliaries have three common characteristics.

1. They are never used alone. A principal verb is either present or implied.

• I can fly an aeroplane.
• He should behave.
• Will you go? Yes, I will (go).

2. Modal auxiliaries have no –s in the third person singular.

• I can swim.
• She can swim. (NOT She cans …)
• I may pass.
• He may pass.
• They may pass.

3. Modal auxiliaries do not have infinitives (to may, to shall etc.) or participles (maying, shalling, shalled etc.). You cannot say to shall, to must or to may.

The structure of the past perfect tense is:

For negative sentences in the past perfect tense, we insert not between the auxiliary verb and main verb. For question sentences, we exchange the subject and auxiliary verb. Look at these example sentences with the past perfect tense:

When speaking with the past perfect tense, we often contract the subject and auxiliary verb:

The past perfect tense expresses action in the past before another action in the past. This is the past in the past. For example:

• The train left at 9am. We arrived at 9.15am. When we arrived, the train had left.

Look at some more examples:

• I wasn't hungry. I had just eaten.
• They were hungry. They had not eaten for five hours.
• I didn't know who he was. I had never seen him before.
• "Mary wasn't at home when I arrived."
  "Really? Where had she gone?"

You can sometimes think of the past perfect tense like the present perfect tense, but instead of the time being now the time is past.

For example, imagine that you arrive at the station at 9.15am. The stationmaster says to you:

• "You are too late. The train has left."

Later, you tell your friends:

• "We were too late. The train had left."

We often use the past perfect tense in reported speech after verbs like said, told, asked, thought, wondered:

Look at these examples:

• He told us that the train had left.
• I thought I had met her before, but I was wrong.
• He explained that he had closed the window because of the rain.
• I wondered if I had been there before.
• I asked them why they had not finished.