Both

1. 'Both' refers to two things or people together - it is equivalent to "one and the other"

• Both cars are red (The two cars are red)
• Both children were born in Italy (The two children were born in Italy)

2. It can be used with plural nouns on its own, or it can be followed by 'of' 

• Both her brothers are living in Canada / Both of her brothers are living in Canada

3. When followed by a plural pronoun (us, you, them), 'both' must be followed by 'of' 

• Both of us like swimming (correct) / Both us like swimming (incorrect)
• Both of you should come to the party (correct) / Both you should come to the party (incorrect)
• I spoke to both of them (correct) / I spoke to both them (incorrect)