We characterize horizontal mixing and transport structures in the surface circulation of the Mediterranean Sea, as obtained from a primitive equation circulation model. We calculate the Finite Size Lyapunov Exponents (FSLEs) of the velocity data set, which give a direct measure of the local stirring. By proper election of the FSLE parameters, we focus on the mesoscale structures, locating a number of vortices embedded in an intricate network of high-stretching lines. These lines control transport in the system. At the edge of the vortices, a dense tangle of line intersections appears, identifying strong mixing. The spatial distribution of FSLEs, averaged over one year, allows to classify areas in the Mediterranean basin according by their mixing activity. The space average of FSLEs on selected geographical regions gives a measure for quantifying and comparing the mixing seasonal variability.