To May

1. (obsolete, intransitive) To be strong; to have power (over). [8th–17th c.]
2. (obsolete, auxiliary) To be able; can. [8th–17th c.]
3. (intransitive, poetic) To be able to go. [from 9th c.]
4. (modal auxiliary verb, defective) To have permission to, be allowed. Used in granting permission and in questions to make polite requests. [from 9th c.]

Synonyms: can, could, might

5. (modal auxiliary verb, defective) Expressing a present possibility; possibly. [from 13th c.]

Synonyms: could, might

6. (subjunctive present, defective) Expressing a wish (with present subjunctive effect). [from 16th c.]

Synonym: might

7. Used in modesty, courtesy, or concession, or to soften a question or remark.

May is now a defective verb. It has no infinitive, no past participle, and no future tense. Forms of to be allowed to are used to replace these missing tenses.

The simple past (both indicative and subjunctive) of may is might

The present tense is negated as may not, which can be contracted to mayn't, although this is old-fashioned; the simple past is negated as might not, which can be contracted to mightn't.

May has archaic second-person singular present forms mayest and mayst.

Usage of this word in the sense of possibly is considered incorrect by some speakers and writers, as it blurs the meaning of the word in the sense have permission to. These speakers and writers prefer to use the word might instead.

Wishes are often cast in the imperative rather than the subjunctive mood, not using the word may, as in Have a great day! rather than May you have a great day.