This book presents a comprehensive account of molecular quantum electrodynamics from the perspectives of physics and theoretical chemistry. The first part of the book establishes the essential concepts underlying classical electrodynamics, using the tools of Lagrangian and Hamiltonian mechanics. The second part focuses on the fundamentals of quantum mechanics, particularly how they relate to, and influence, chemical and molecular processes. The special case of the Coulomb Hamiltonian (including the celebrated Born-Oppenheimer approximation) is given a modern treatment. The final part of the book is devoted to non-relativistic quantum electrodynamics and describes in detail its impact upon our understanding of atoms and molecules, and their interaction with light. Particular attention is paid to the Power-Zienau-Woolley (PZW) representations, and both perturbative and non-perturbative approaches to QED calculation are discussed. This book is ideal for graduate students and researchers in chemical and molecular physics, quantum chemistry, and theoretical chemistry.