All or all of?

Short answer: prefer  all, without of


The of (the "partitive genitive") is almost always unnecessary. Thus, all people, all countries, all the time, all students, all computers, all hope, all the money instead of all of the people, all of the countries etc.

It is not that, say,  all of the students is never used,  but this partitive formulation has a specific emphatic function, and is almost equivalent to saying each and every single one of the students. It draws attention to their identity as individuals  rather than as members of a group.   

Exception: Use all of if the next word is a pronoun (me, you, him, her, it, us, them)

The Frank Sinatra song All of me might help you remember this exception.