Ability: can, could.
Permission: may, could, can.
Advice: should, ought to.
Criticism: should, ought to.
Obligation and necessity: must/ have to/ need to; needn't/ don't have to/ don't need to; had to; needn't / didn't have to/ didn't need to.
Degrees of certainty: must/can't/ couldn't; should, ought to; should, ought to; could; may; might.