Modal verbs are helping verbs that indicate likelihood, permission, ability, obligation, or advice. Unlike normal verbs, modals do not take -s in third person and are followed by the bare infinitive (verb base form without 'to').
Core Modals & Their Exact Uses
Can vs. Could
Can expresses present ability (I can swim). Could expresses past ability (I could run fast when young) or polite requests (Could you help me?).
May vs. Might
May expresses permission or high possibility (50%). Might expresses low or remote possibility (20-30%).
Must vs. Should
Must indicates strong obligation or logical certainty (You must stop at red lights). Should indicates mild recommendation or moral advice (You should sleep early).