Title: Theoretical and computational problems for the equations of the ocean and the atmosphere Abstract: In this lecture we will present some theoretical and computational problems encountered in the equations of the ocean and the atmosphere. The theoretical results include questions of existence and uniqueness of solution for the Primitive Equations of the Ocean and the Atmosphere in the absence of viscosity. Some of the computational questions that will be addressed, in particular the question of the boundary conditions, have a more general interest in engineering and sciences.