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