Modals and their meanings
can
General ability (present)
Informal requests or permission
could
General ability (past)
Polite, informal requests or suggestions
may
Formal requests or permission
Possibility
might
Possibility
must
Necessity (present or future)
Strong possibility or near certainty (present or past)
should
Suggestions or advice
Obligations or duties
Expectations
will*
Certainty
Requests
Promises and offers
would
Polite requests
Habitual or repeated actions (past)
* Shall traditionally was the modal used with I or we in place of will. It is now used mainly for polite requests or in very formal contexts (Shall I call you soon?).