Both,both…and,both of的用法及区别?

sb both do sth 例：we both like study 我俩都爱学习
both A and B do sth 例如：both he and I like study 他和我都爱学习
both of A and B do sth 例如：he and I are classmates ,both of us like study 他和我是同学,我俩都爱学习.
both 特指两个人,both…and...做主语所以用I he ,both of 做伴随,所以用us him me这种