(modal, auxiliary verb, defective) Used before a verb to indicate the simple future tense in the first person singular or plural.
I hope that we shall win the game.
Used similarly to indicate determination or obligation in the second and third persons singular or plural.
(determination): You shall go to the ball!
Used in questions with the first person singular or plural to suggest a possible future action.
Let us examine that, shall we?
To owe.