Affirmative (+) form
May comes first in the verb phrase (after the subject and before another verb):
It may be possible for him to get home tonight.
May can’t be used with another modal verb:
This may hurt you.
This may could hurt you. or This could may hurt you.
Negative (−) form
The negative form of may is may not. We don’t use don’t/doesn’t/didn’t with may:
We may not have enough information at the moment.
We don’t may have enough information at the moment.
We don’t use mayn’t as the contracted form of may not:
We may not yet know what is safe to eat.
We mayn’t yet know what is safe to eat.
Question (?) form
The subject and may change position to form questions. We don’t use do/does/did:
May we drop you at your hotel?
Do we may drop you at your hotel?
May I leave the room, please?
Do I may leave the room please?
We use may to ask for, give and refuse permission. It is quite formal.
asking for permission
Can, could and may are all used to ask for permission. May is the most formal/polite and could is more formal and polite than can.
We use may to refer to weak possibility in the present and future:
The economy may go up or down in the next year. (I think both are possible, the economy going up or the economy going down. I am not making either one a strong possibility.)
I think I may go to the doctor today and try to get some antibiotics. (I am not very sure yet if I will go to the doctor.)
We use may in formal writing, especially academic English, to describe things which the speaker thinks are generally true or possible. In this case, it is a more formal equivalent of can.
Both sentences express what the speaker believes to be a general truth about where the cottage is located. The speaker knows that there is a cottage in the museum and a visitor is able to see them there if they want to. May is more formal.
Accepting a different view or opinion
We often use may to accept a different view or opinion, especially with well, and/or followed by but:
One month may well be too long to go away on holiday.
I may be wrong but I am going to tell the police about it.
The couch may well cost more but it’s going to be different.