Attaches to the negative stem (nai-stem) of verbs; for サ変 verbs, use せずに. Expresses that an action is not performed while another action occurs. Often interchangeable with ないで, but ずに is slightly more formal or literary.
See also: ないで
I went to school without eating breakfast.
He left the room without saying anything.
It's impossible to take the exam without studying.