This text is an introduction to electrophysiology, following a quantitative approach. The first chapter summarizes much of the mathematics required in the following chapters. The second chapter presents a very concise overview of the general principles of electrical fields and current flow, mostly es- tablished in physical science and engineering, but also applicable to biolog- ical environments. The following five chapters are the core material of this text. They include descriptions of how voltages come to exist across membranes and how these are described using the Nernst and Goldman equations (Chapter 3), an examination of the time course of changes in membrane voltages that produce action potentials (Chapter 4), propagation of action potentials down fibers (Chapter 5), the response of fibers to artificial stimuli such as those used in pacemakers (Chapter 6), and the voltages and currents produced by these active processes in the surrounding extracellular space (Chapter 7). The subsequent chapters present more detailed material about the application of these principles to the study of cardiac and neural electrophysiology, and include a chapter on recent developments in mem- brane biophysics. The study of electrophysiology has progressed rapidly because of the precise, delicate, and ingenious experimental studies of many investigators. The field has also made great strides by unifying the numerous experimental observations through the development of increasingly accurate theoretical concepts and mathematical descriptions. The application of these funda- mental principles has in turn formed a basis for the solution of many different electrophysiological problems.