1. There is no semantic difference when shall and will are used to refer to the simple future. Will can be used in all persons. In informal spoken English, remember that the affirmative contraction is 'll and the negative contraction is won't. There is no contracted form in the interrogative. Examples of usage might be:
'The Government will consider lowering the age of consent from 16 to 15.' (formal)
'I don't know if I can come, but I'll let you know by Thursday.' (informal)
'Where will you be on Thursday? Will you be at home?' (informal)
Shall is also sometimes used in the first person when it has the same meaning as will. In informal spoken English, the affirmative contraction is again 'll and the negative contracted form is shan't.
'I shall never finish this essay - I've still got 2,000 words to write!'
'I'll never finish this homework - I'm tired and I want to go to bed!'
'I shan't ever be good enough to go to university - I just haven't got the brains!'
Shall is often used in questions in the first person singular and plural when making suggestions, making an offer or asking for advice:
'Shall we go out for dinner tonight?'
'Shall I get more tomato juice when I'm at the supermarket?'
'What shall we do now? We're clearly not going to get there by nightfall.'
However, when we want to express a strong intention to do something, we use will or 'll in the first person singular and plural:
'Is that somebody at the door? I'll just go and see who it is.'
'We'll get the cakes for the coffee morning tomorrow, Jane.'
'No, no. I will. I'm the hostess, after all.'
2. There are three uses of should and would. Referring to the present or future, should is often used as an alternative to shall in connection with requests for advice or instruction:
'What do you think I should do now? Should I write him a letter, send him an e-mail, or should I try to phone him up?'
Should is often used to talk about obligation and duty as an alternative to 'ought to':
'If you are still infectious, you should stay at home. You shouldn't be out and about, infecting everybody you meet.'
'You really should open a bank account. You shouldn't keep so much money in the house.'
'People with fierce dogs should keep them on a leash at all times.'
Should is used after if when a slight possibility is suggested.
'If you should see her at the anniversary concert, do give her my best regards.'
'If I should bump into Tony, do you want me to remind him that he still owes you one hundred pounds?'
3. Would (or the contracted form 'd) is sometimes used as an alternative to 'used to' when discussing past habits:
'When we were young, we would spend (we'd spend) every summer holiday at the sea-side.'
'You would find him (you'd find him) sitting at the bar every lunchtime, drinking that strong black beer and chatting to the bartender until one day he was there no longer.'
Would is also used to make polite requests:
'Would you be prepared to do all this work by yourself without any assistance?'
'Would you (be so kind as to) pick Jennifer up from school on Monday?'
Would (or its contracted form 'd in conversational English) is also associated with the conditional in its simple, progressive, perfect and passive aspects:
'There's no doubt about it. I would definitely (I'd definitely) travel to Mexico with you, if I could afford it.'
'You would still be (you'd still be) working for the World Bank, if you hadn't kicked up such a fuss.'
'I would have told you (I'd have told you) all about it, if you had phoned me.'
'If you wore smarter clothes, you would be invited (you'd be invited) to all the press conferences.'
