We report on detailed first-principles calculations which focus on the magnetic and structural properties of the (0001) surface of gadolinium. The electronic correlation within the localized 4f states is treated within the self-interaction correction (SIC), thus going beyond the local spin-density approximation. The ferromagnetic ground state is predicted correctly if the SIC is temperature are addressed by Monte Carlo calculations. The SIC also has a profound effect on the dispersion of the d surface states, due to hybridization of the 4f states with the 5d valence states. The best agreement with photoemission experiments is obtained within the transition state approximation, which takes into account the orbital relaxation. The Rashba spin-orbit coupling in the d surface states is fully captured by our relativistic multiple scattering approach.