Preface; M1. Algebra of vectors; M2. Vector functions; M3. Differential relations; M4. Coordinate transformations; M5. The method of covariant differentiation; M6. Integral operations; M7. Introduction to the concepts of nonlinear dynamics; 1. The laws of atmospheric motion; 2. Scale analysis; 3. The material and the local description of flow; 4. Atmospheric flow fields; 5. The Navier-Stokes stress tensor; 6. The Helmholtz theorem; 7. Kinematics of two-dimensional flow; 8. Natural coordinates; 9. Boundary surfaces and boundary conditions; 10. Circulation and vorticity theorems; 11. Turbulent systems; 12. An excursion into the spectral turbulence theory; 13. The atmospheric boundary-layer; 14. Wave motion in the atmosphere; 15. The barotropic model; 16. Rossby waves; 17. Inertial and dynamic stability; 18. The equation of motion in general coordinate systems; 19. The geographical coordinate system; 20. The stereographic coordinate system; 21. Orography-following coordinate systems; 22. The stereographic system with a generalised vertical coordinate; 23. A quasi-geostrophic baroclinic model; 24. A two-level prognostic model: baroclinic instability; 25. An excursion into numerical procedures; 26. Modeling of atmospheric flow by spectral techniques; 27. Predictability; Answers to problems; List of commonly used symbols; References; Index.