This book is an indispensable guide to the methods used by nearly all major weather forecast centers in the United States, England, Japan, India, France, and Australia. Designed for senior-level undergraduates and first-year graduate students, the book provides an introduction to global spectral modeling. It begins with an introduction to elementary finite-difference methods and moves on towards the gradual description of sophisticated dynamical and physical models in spherical coordinates. Topics include computational aspects of the spectral transform method, the planetary boundary layer physics, the physics of precipitation processes in large-scale models, the radiative transfer including effects of diagnostic clouds and diurnal cycle, the surface energy balance over land and ocean, and the treatment of mountains. The discussion of model initialization includes the treatment of normal modes and physical processes, and the concluding chapter covers the spectral energetics as a diagnostic tool for model evaluation.