This is an introductory text on numerical weather prediction (numerically modelling the general circulation of the atmosphere), utilizing the spectral transform method. The book covers finite difference methods and time-differencing schemes; the theoretical development of the spectral transform method (using spherical surfaces rather than grids for determining variation in the elements of weather); physical processes; current issues in dynamical and physical initiation; and data analysis. Several practical examples of the spectral transform method are included.