Cambridge Grammar of English Hardback with cd-rom a comprehensive Guide

Obligation and invitations

Must

expressing obligation is quite strong, but it is also used to express polite

invitations:

You 

must get those done by tomorrow.

I told her she 

must keep her door locked at all times.

A: You must come down and have a meal with us sometime.

B: Yeah.

(polite invitation)

Rules and laws

Must

and must not often occur in public signs and notices indicating laws, rules

and prohibitions:

[airline website information]

All passengers 

must present valid photo identification at check-in for all flights.

[public notice at a railway station]

Passengers 

must not cross the line.

Reproaches

Must

in the interrogative form is used to issue reproaches and often expresses a

feeling of exasperation on the part of the speaker:

Must you have that music so loud?

Why 

must people always park right across our exit?