The goal of this talk is to construct smooth solutions of the Magnetohydrodynamics equations (MHD) that show a change in the topological structure of magnetic field lines. This is known to be impossible in the non-resistive case by Alfvén’s theorem, indeed the integral lines of a sufficiently smooth magnetic field are transported by the fluid. The reconnection of the magnetic field lines occurs instead in the resistive case, being responsible for many dynamic phenomena in astrophysics such as solar flares and the solar wind. Although numerical and experimental evidence exist, analytical examples of magnetic reconnection were not known.