This monograph offers a comprehensive examination of the Lambert W function and its significant applications in solving nonlinear engineering problems, particularly within the field of power engineering. It bridges the gap between advanced mathematical theory and practical engineering implementation. The work begins with a thorough introduction to the mathematical properties of the Lambert W function, covering various numerical solution techniques, including Newton's and Halley's methods, asymptotic approximations, and Taylor expansions. It also introduces the closely related g-function (LogWright function), which serves as an effective alternative in cases where the numerical evaluation of the Lambert W function encounters difficulties. Special attention is given to practical tools, including MATLAB code implementations provided for selected sections. The book demonstrates the function's wide-ranging applications: from solar cell and perovskite solar cell modeling, analytical air-gap length calculation in inductors, and the no-load startup of induction machines, to diode-resistor circuits, rectifier systems, and proton-exchange membrane fuel cells. Rich in examples, code, and theoretical depth, it is intended for researchers, postgraduate students, and engineers aiming to apply precise and elegant analytical methods in power system modeling.