Shall 有四種用法。
1. 只用在第一人稱，等於will，表示未來式。He will go to the cinema. I shall/will go to the cinema.
2. 表示強烈的意願。They shall go to the cinema. 他們非常非常想去電影院，會盡一切能力辦到。如果是用在第一人稱，像是 I shall go to the cinema 會有兩種意思。一個是像上面那一種，單純表示未來式。第二種意思則是表現強烈的意願。所以如果是 I shall 的話，要看上下文章來決定是什麼意思。
3. 表示強烈的命令。You shall not kill. 這裡的shall意思跟must意思接近。
4. 用在疑問句，表示建議，用在第一人稱。Shall I close the door? Shall we go? 第二三人稱用will。Will you please cover for me? Will you open the door?
Shall 的過去式為 should，但是 should也有自己的意思，如下：
1. 表示應該。You should be nice to others. Students should not cheat on tests. He should not have told her the secret.
這裡 Students should not cheat on tests 跟 Students shall not cheat on tests做一個比較。前者是學生不應該作幣，語氣上比後者平和，是說明一個一般的狀況。後者是shall的第三種用法，意思為學生不可以作幣，語氣上很強烈，可能學校老師會說的警告的話。
2. 表示很高的可能性，One hour should be enough for him to get to the office. The project should be easy to complete. Should you change your mind, call me.
3. 用在不可能的假設語氣。如果是現在不可能的話，If I had money, I should try to help him. 如果是過去不可能的話，If I had had money, I should have tried to help him.
如果是可能的假設語氣，則是用shall/will。If I have money, I will/shall try to help him.
假設語氣的用法，另外參考「假設語氣」那一篇文章。
4. 表示驚訝的語氣。
I am surprised that he should be so angry about such a small thing.
= I am surprised that he is so angry about such a small thing.
You should have seen his face when he discovered the truth.
5. 用來強調。
In order that your preparation for taking the TOEFL should be effective, you need to set up a plan.
= In order that your preparation for taking the TOEFL is effective, you need to set up a plan.
A: The team is going to lose again. B. I should hope not.
= A: The team is going to lose again. B. I hope not.
Should have 表示當時應該做某件事情，
1. 用於假設語氣中的過去不可能。
可能的假設：If it rains, I will/shall bring my umbrella.
現在不可能：If it rained, I should bring my umbrella.
過去不可能：If it had rained, I should have brought my umbrella.
假設語氣的用法，參考假設語氣的那一篇文章。
2. 表示當時應該做。I should have studied harder. You should not have done that.
Will 的用法跟 shall類似。
1. 表示未來式。第一人稱用shall，第二三人稱用will。參考shall的第一種用法。He will go to the cinema. I shall/will go to the cinema.
2. 用在疑問句，表示建議。用法跟shall的第四種類似。第一人稱用shall。Shall I close the door? Shall we go? 第二三人稱用will。Will you tell me what is happening? Will you open the door?
3. 表示一定會發生或是高度可能會發生的事或是有能力辦到的事。Accidents will happen if you drink and drive. Your new car will go up to 300km/hr.
Would 為will 的過去式，但是would 也有自己的意思。
1. will的過去式。
I will travel to America in a few days. 從現在開始算，表示未來。
I would travel to America in a few days. 從過去的一個時間點開始算，表示當下的未來。
2. 用在假設語氣。
可能的假設：If I know the truth, I will tell her.
現在不可能：If I knew the truth, I would tell her.
過去不可能：If I had known the truth, I would have told her.
另外還一種假設語氣的用法，用would that ，表示意願或希望。
Would that she had seen her baby before she died.
= I hope that she had seen her baby before she died.
Would that I could take a long vacation.
= I hope that I could take a long vacation.
3. 表示建議, 提議，意願，或希望。I would not smoke if I were you. Would you give us some coffee please? I would love to go with you. Would you rather live by the sea or in the mountains? I would hope prices have gone down.
Would have 通常用在假設語氣。
可能的假設：If I know the truth, I will tell her.
現在不可能：If I knew the truth, I would tell her.
過去不可能：If I had known the truth, I would have told her.
Can/could/could have
1. 表示能力，用法同be able to。
He can speak several languages.
= He is able to speak several languages.
如果是過去式，用could，表現過去有能力。
He could speak several languages.
= He was able to speak several languages.
2. 表示可能性。
比較以下三句：
We can have Italian food tonight.
We could have Italian food tonight.
We could have had Italian food.
第一句表示能力，或是表示一般的可能性。意思可能為，有材料做義大利料理，或是有能力做義大利料理，或是一般性的義大利料理是晚餐的選項之一。
第二句表示意願，或是建議。意思為有意願吃義大利料理，或是建議吃義大利料理。
第三句表示意願，或是建議，但是是當時的意願或建議。
再比較以下兩句：
You can learn English by reading articles on BBC.
You could learn English by reading articles on BBC.
前者表示你有能力，還是這是選項之一。後者表示這是一個建議。
3. 表示提議，命令。
比較以下兩句：
Can you open the door for me?
Could you open the door for me?
前者的語氣比較不客氣，像是上對下的提議或命令。後者為客氣的疑問。
I can make you some coffee.
I could make you some coffee.
前者為提議，後者為很客氣的提議。
4. 表示被准許做某件事，用法同be allowed to。
He can leave work early today. = He is allowed to leave work early today.
He could not leave work early yesterday. = He was not allowed to leave work early yesterday.
5. 用在假設語氣
可能的假設：I can leave early today if I ask my boss.
現在不可能：I could leave early today if I asked my boss.
過去不可能：I could have left early if I had asked my boss.
May/might/might have
1. 用法跟can/could/could have的第三種用法類似，表示提議或命令，但是語氣上更為客氣。
Can you open the door for me?
Could you open the door for me?
May you open the door for me?
Might you open the door for me?
上面四句，語氣愈來愈客氣。第一種為一般用法，語氣上比較不客氣，或是為命令。第二種跟第三種最常見，語氣很客氣。第四種不太常見，因為太過客氣，用在可能性很低所以要比較低聲下氣，或是很不願意打擾對方的狀況。
2. 用法跟can/could/could have的第二種用法類似，表現可能性。
We could have Italian food tonight.
We might have Italian food tonight.
兩者都是講可能性，前者的可能性比較高。
We could have won the game.
We might have won the game.
前者的可能性比較高。
We use the modal can to make general statements about what is possible:
If we don’t hurry we could be late. (=Perhaps/Maybe we will be late)
We use could have to show that something is/was possible now or at some time in the past:
It can be very cold in winter. (= It is sometimes very cold in winter)You can easily lose your way in the dark. (= People often lose their way in the dark)
We use could as the past tense of can:
It could be very cold in winter. (=Sometimes it was very cold in winter.)
You could lose your way in the dark. (=People often lost their way in the dark)
We use could to show that something is possible in the future, but not certain:You could lose your way in the dark. (=People often lost their way in the dark)
If we don’t hurry we could be late. (=Perhaps/Maybe we will be late)
We use could have to show that something is/was possible now or at some time in the past:
It’s ten o’clock. They could have arrived now.
They could have arrived hours ago.
- See more at: https://learnenglish.britishcouncil.org/fr/comment/80669#sthash.hNvsJ0Qf.dpufThey could have arrived hours ago.
