modals

are auxiliary verbs that are used with main verbs to give advice and express ideas like ability, necessity, possibility, 

can

could(more formal)

may(most formal)

must

have to

should

 expresses a strong obligation or necessity

often shows us that obligation comes from the speaker

shows that the obligation comes from outside the speaker

sometimes called as "external obligation"

not compulsary

no obligation

stated in the past

can't

must not/mustn't

should not/shouldn't

against the rules particularly when we didn't make the rules

talk about what is not permitted

common on public signs and notices informing people of rules and laws

particularly when the prohibition comes from the speaker.

give advice or to talk about what we think is wrong