Magnetohydrodynamics (MHD) is the study of electrically conducting flux (salt water, plasma...) subject to an electromagnetic field. We model it with two coupled partial differential equations: the Navier-Stokes equations and the Maxwell equations. In this lecture, in a first time we will understand the building of this model and applications in different fields, and in a second time we will discuss about the existence and unicity of solutions for different types of boundary conditions (Navier, on the pressure, Dirichlet ...).