The discovery of neutrino oscillations is arguably the most significant recent discovery in high energy physics. A neutrino factory is the most precise and powerful machine that can study the properties of neutrinos. I will first outline the physics of neutrino oscillation. I will point out aspects of that physics which effect the design of the neutrino factory and its detectors. I will then describe the design of a neutrino factory, including its advantages over other methods for producing neutrinos. I will go into some detail on the design principles and challenges of the various subsystems of a neutrino factory.