(in the first person) expressing the future tense

this time next week I shall be in Scotland

we shan't be gone long

expressing a strong assertion or intention

they shall succeed

you shall not frighten me out of this

expressing an instruction, command, or obligation

every employer shall take all practicable steps to ensure the safety of employees

you shall not steal

used in questions indicating offers or suggestions

shall I send you the book?

shall we go?