Neurophysiology historically began with Luigi Galvani in 1791 when he published the monograph "De Viribus Electricitatis in Motu Musculari Commentarius" (Commentary on the Effect of Electricity on Muscular Motion). This monograph suggested an inherent electricity exists within the living tissue.
The study of nervous system electrophysiology can occur at many different levels including: 1) Electroencephalography (EEG) 2) Local Field Potentials 3) neuron populations and 4) the electrical activity outside or inside a neuron measured by patch clamp methods. As such, the major focus of this field is on cellular communication. Frequently studied as the generation of electrical signals within neurons from the regulated flow of various ions, often in the form of an action potential. A good beginning reference is the "Physiology of the Nervous System" by David Ottoson.