Can
ability, doubt, permission, polite request
May
permission, future possiblity
Must
obligation, firm necessity, logical conclusion
Have to
unwillingness, forced circumstances
Will
wish, desire, will, certain prediction, promise
Shall
intention, supposition, suggestion
Ought to
moral duty, strict recommendation
Be to
obligation arising out of arrangement
Would
invitation, polite request, a habit of the past
Should
advice, uncertain prediction, recommendation
Need
(un)necessity
Used to
repeated action in the past