To form the first person imperative, we put let before me and us:
There is a negative form:
Let can also be used with the third person:
But the negative form is not used in modern English.
The following form is used to talk about somebody's decisions. For example official arrangements:
Or orders given by other people:
But it can also be used to give orders in the third person:
Will is mainly used by people who have some authority, e.g. captains of ships, headmasters of schools etc.:
Let is also used for asking for permission:
The meaning depends on the context.
Be to can also be used to talk about destiny:
Be to is used in the present and past simple. It also has a perfect form, but it's only used for past unfulfilled plans:
The be to form can also be used with the second conditional to indicate that the sentence refers only to the future:
And in very formal situations:
This change in word order is similar to: