Introductory description of the Erath’s climate system, governing equations of mass and momentum conservation, equation of state, thermodynamic equation, wave kinematics, dispersion, group velocity, sound waves, gravity waves, effect of rotation, equations of motion in spherical coordinates, primitive equations, Bussinesq approximation, changing vertical coordinate, asymptotic analysis and scaling, geostrophic balance, thermal wind, static instability, boundary layers in atmosphere and ocean.