pt. 1. Mathematical tools. Algebra of vectors -- Vector functions -- Differential relations -- Coordinate transformations -- The method of covariant differentiation -- Integral operations -- Introduction to the concepts of nonlinear dynamics -- pt. 2. Dynamics of the atmosphere. The laws of atmospheric motion -- Scale analysis -- The material and the local description of flow -- Atmospheric flow fields -- The Navier-Stokes stress tensor -- The Helmholtz theorem -- Kinematics of two-dimensional flow -- Natural coordinates -- Boundary surfaces and boundary conditions -- Circulation and vorticity theorems -- Turbulent systems -- An excursion into spectral turbulence theory -- The atmospheric boundary layer -- Wave motion in the atmosphere -- The barotropic model -- Rossby waves -- Inertial and dynamic stability -- The equation of motion in general coordinate systems -- The geographical coordinate system -- The stereographic coordinate system -- Orography-following coordinate systems -- The stereographic system with a generalized vertical coordinate -- A quasi-geostrophic baroclinic model -- A two-level prognostic model, baroclinic instability -- An excursion concerning numerical procedures -- Modeling of atmospheric flow by spectral techniques -- Predictability.