May
Can / Could / Dare / Have to / May / Might / Must / Need (to) / Ought to / Shall / Should / Use(d) to / Will / Would
Review Modal verbs by function here
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Possibility
Ask or give permission (formal)
General Truths (formal)
Accepting different opinions
Function
Possibility
We use "May" to express a slight or slim possibility in the present or future:
They may still win the election, even if the opinion polls give the opposition a 40% lead.
I think I may be able to go to the concert if my parents lend me the money.
It may be possible to find the parts to fix your car, but they are very rare.
See also Might, Could, Can
Permission
We often use "may" to ask for, give or refuse permission. It is a more formal and polite than "could" or "can"
May I speak with her Highness?
No, you may not.
See also Could, Can
General Truths
"May" is used, especially in formal wirting, to express something we consider to be generally true. It is a more formal alternative to "can" in this use.
Such policies may result in economic harship for the local community.
It may not be possible to correct this course of action
See also: can
Accepting different opinions
"May" can be used to give qualified or cautious agreement with something. This is often used with "well" and "but", often with a conditional clause clarifying our cynicism of the position.
You may well think that but I couldn't possibly comment.
You may well be right but if it turns out you were wrong then don't come crying to me.
It may well be true that the prospects are positive, but if you consider the evidence I have submitted, you may well change your mind.