The cost to the world's economy due to corrosion was said to be two and a half trillion dollars or 3.4% of global GDP in 2013. Electrochemistry as a discipline is of even greater relevance ten years on, in view of the world's desperate attempts to prevent catastrophic climate change by moving from fossil fuel to "e-mobility" among other measures. This means that whereas electrochemistry in all its mystery and complexity was formerly the domain of the physical chemist alone, today it is an essential skill for the materials scientist, the engineer and indeed the physicist. This textbook fills a gap in providing a course of learning from first principles for the student, researcher and industrialist who has an undergraduate-level education in physics but only high school chemistry. The author will take you through simple electrochemical cells and the rigorous description of the many confusing "potentials" that arise across their interfaces, to what can and cannot be measured in an experiment. The first three quarters of the book are rather general, highlights being the electrochemical series and the Nernst and Butler-Volmer equations. This all lies at the heart of the science of corrosion, fuel cells and batteries. The last quarter of the book is dedicated solely to corrosion, applying the thermodynamic and kinetic groundwork laid earlier to help the reader clearly understand the two principal tools of corrosion scientists and engineers: the Evans and Pourbaix diagrams.