Definitions:
used to indicate obligation, duty, or correctness, typically when criticizing someone's actions

used to indicate what is probable

(expressing the conditional mood) referring to a possible event or situation

used in a clause with ‘that’ after a main clause describing feelings

used in a clause with ‘that’ expressing purpose

(in the first person) expressing a polite request or acceptance

(in the first person) expressing a conjecture or hope

used to emphasize to a listener how striking an event is or was