Modal auxiliary verbs can express various aspects of obligation and freedom. Note that the use of modals verbs can help in making a request, suggestion or instruction sound more polite.

Strong obligation

To express strong obligation, we use must.

All staff must arrive for work by 8 am.

The auxiliaries will and need can also express strong obligation. Will, for example, can be used to give orders.

Need I wait any longer?
The staff will arrive for work on the coming Sunday.

Prohibition

Must not, cannot and may not can be used to express prohibition.

Vehicles must not be parked in front of the gate.
You can’t go now.

Weak obligation

Should, ought to and had better can be used to express weak obligation. These auxiliaries can also be used to make a recommendation or suggestion.

You should respect your parents and teachers.
We ought to help the poor and the needy.
You had better mend your ways.
We had better buy a new fan.

Willingness

To express willingness, shall and will can be used.

Shall I give you a hand?
I will pay for the snacks.

Permission

To ask for permission, we can use may or can.

May I go now?
May I come in?
Can I borrow your car?