Can - denotes a. ability, b. permission or request, or c. possibility.
Will - indicates a. futurity, or b, willingness or choice
Would - expresses a. willingness in a potential way, b. polite question requests, c future intention from the past point of view, or d. past habitual action
Shall - expresses suggestion in a yes-no question
Should - expresses obligation
May - expresses a. permission, b. probability, or c. wish
Might - used to express less probability
Must - used a. to express very strong obligation or necessity, b. making an inference or logical conclusion
Modal Verbs - helping verbs that modify or change the meaning of the main verbs. You use modal verbs in giving advice or suggestions, in making requests, or in giving predictions and prohibitions.
Modal Nouns - expresses the quality or state in some manner other than a simple face.
Modal Adverbs - describe how something is done and how someone feels about something.