This book provides a comprehensive overview of numerical weather prediction NWP, focusing on the application of the spectral method in NWP models. The author illustrates the use of the spectral method in theory as well as in its application to building a full prototypical spectral NWP model, from the formulation of continuous model equations through development of their discretized forms to coded statements of the model. The author describes the implementation of a specific model - PEAK Primitive-Equation Atmospheric Research Model Kernel - to illustrate the steps needed to construct a global spectral NWP model. The book brings together all the spectral, time and vertical discretization aspects relevant for such a model. Spectral Numerical Weather Prediction Models provides readers with the information necessary to construct spectral NWP models, a self-contained, well-documented, coded spectral NWP model and theoretical and practical exercises, some of which include solutions.