The rule below about shall/will  also applies to should/would, as described at the end.

People may sometimes tell you that there is no difference between shall and will , or even that today nobody uses shall  (except in offers such as Shall I call a taxi?). This is not really true. The difference between shall and will  is often hidden by the fact that we usually contract them in speaking with 'll . But the difference does exist.

The truth is that there are two  conjugations for the verb will:

1st conjugation (objective, simple statement of fact)
personverbexampleexample contraction
IshallI shall be in London tomorrow.I'll
youwillYou will see a large building on the left.You'll
he, she, itwillHe will be wearing blue.He'll
weshallWe shall not be there when you arrive.We shan't
youwillYou will find his office on the 7th floor.You'll
theywillThey will arrive late.They'll
2nd conjugation (subjective, strong assertion, promise or command)
personverbexampleexample contraction
IwillI will do everything possible to help.I'll
youshallYou shall be sorry for this.You'll
he, she, itshallIt shall be done.It'll
wewillWe will not interfere.We won't
youshallYou shall do as you're told.You'll
theyshallThey shall give one month's notice.They'll

It is true that this difference is not universally recognized. However, let those who make assertions such as "Americans never use 'shall'" peruse a good US English dictionary, or many US legal documents which often contain phrases such as:

  • Each party shall¬†give one month's notice in writing in the event of termination.

Note that exactly the same rule applies in the case of should and would. It is perfectly normal, and somewhat more elegant, to write, for example:

  • I should¬†be grateful if¬†you would¬†kindly send me your latest catalogue.

sources : Original Link