This primer seeks to provide an introduction to the science of equilibrium electrochemistry; specifically it addresses the topics of electrode potentials and their applications. It builds on a knowledge of elementary thermodynamics giving the reader an appreciation of the origin of electrode potentials and shows how these are used to deduce a wealth of chemically important information and data such as equilibrium constants, the free energy, enthalpy and entrophy changes of chemical reactions, activity coefficients, the selective sensing of ions. The emphasis throughout is on understanding the foundations of the subject and how it may be used to study problems of chemical interest. The Primer is directed towards students in the early years of their university courses in chemistry and allied subjects; accordingly, the mathematical aspects of the subject have been minimized as far as is consistent with clarity.