A. both / either / neither (two things or people)
• Rosemary has two children. Both are married. (Both = the two children)
• Would you like tea or coffee? You can have either. (= tea or coffee)
• A: Do you want to go to the cinema or the theatre?
• B: Neither. I want to stay at home. (Neither = not the cinema or the theatre)
Compare either and neither:
'Would you like tea or coffee?'
'Either. I don't mind.' (= tea or coffee)
'Neither.' (= not tea or coffee)
B. both / either / neither + noun
both + plural: both windows/books/children etc.
either / neither + singular: either / neither window/book/child etc.
• Last year I went to Paris and Rome. I liked both cities very much.
• This I worked in an office, and later in a shop. Neither job was very interesting.
• There are two ways from here to the station. You can go either way.
C. both of ... / either of ... / neither of ...
both of these / those ...
either / neither of my / your / Ann's ... etc.
• Neither of my parents is English.
• I haven't read either of these books.
You can say both of (the ...) / both (of) those ... / both (of) my ... etc. (with or without of):
• I like both of those pictures. or I like both those pictures.
• Both of Ann's sisters are married. or Both Ann's sisters are married.
D. both of them / neither of us etc.
both of them
either / neither of us
• Ann has got two sisters. Both of them are married.
• Tom and I didn't eat anything. Neither of us was hungry.
• 'Who are those two people?' 'I don't know either of them.'
both (two things)
Both my parents are teachers. → Both of them are teachers.
I like both these jackets. → I bought both of them.
either / neither (choice or none)
You can have either book. → Take either of them.
Neither answer is correct. → Neither of them is correct.
With of / without of
Both of my friends came. = Both my friends came.
Neither of the shops was open. = Neither shop was open.