0 used to say or ask what is the correct or best thing to do: --
It's rather cold in here. Should I (= do you want me to) turn the heating on?
You shouldn't have said anything.
I should have written to her but I haven't had time.
There should be an investigation into the cause of the disaster.
You should be ashamed of yourselves.
You should take the bus - it's the easiest way to get there.
3 used after "why" when giving or asking the reason for something: --
4 used instead of "would" when the subject is "I" or "we": --
5 used to express surprise in sentences that are in the form of questions: --