This comprehensive resource derives physics-based microscale model equations, then continuum-scale model equations, and finally reduced-order model equations. This book describes the commonly used equivalent-circuit-type battery model and develops equations for superior physics-based models of lithium-ion cells at different length scales. This book presents a breakthrough technology called the discrete-time realization algorithm that automatically converts physics-based models into high-fidelity approximate reduced-order models. These reduced-order models have similar computational complexity to equivalent-circuit-type models, but can also predict electrochemical variables at any spatial location inside the cell.