Both means 'the one and also the other of two persons/things etc'.

• I want both books. 
• Both shirts are good. 

Both and both of

Before a noun with a determiner (the, this, my, your, those etc.) both andboth of are both possible. In American English, both of is common.

• I want both (of) these books.

Before a personal pronoun we use both of. Note that both of is followed by the object form of the pronoun.

• Both of them are good. 
• Both of us want to go.

Note that both of us/you/them can be the subject or object of a clause.

• She has invited both of us. (object) 
• Both of us have been invited. (subject)
• Give my love to both of them. (object) 

Both can be put after pronouns used as objects.

• She has invited us both.
• She has sent you both her love. 

Both and neither

To mean 'none of the two', we use neither, not both…not.

• Neither of them came. (NOT Both of them did not come.) 

We often drop the or a possessive after both.

• You can take both shirts. (NOT…both the shirts.) 
• He lost both parents when he was a child. (NOT … both his parents…)

Position of both

When both refers to the subject of a clause, it can go with the verb. It is put after auxiliary verbs and before other verbs. When there are two auxiliary verbs, both usually goes after the first.

• They are both good.
• We both want to go.
• We have both been invited.
• They have both gone home.

Note that these meanings can also be expressed by using the structureboth (of) + noun/pronoun.

• Both of them are good.
• Both of us want to go.
• Both of us have been invited.
• Both of them have gone home.

Both … and …

The same kind of words or expressions usually follow both and and.

• She is both beautiful and clever. (adjectives)
• She both sings and dances. (verbs)