We report two-photon resonance fluorescence of an individual semiconductor artificial atom. By non-linearly driving a single quantum dot via a two-photon transition, we probe the linewidth of the two-photon processes and show that, similar to their single-photon counterparts, they are close to being Fourier limited at low temperatures. The evolution of the population of excitonic states with the Rabi frequency exhibits a clear s-shaped behavior, indicative of the non-linear response via the two-photon excitation process. We model the non-linear response using a 4-level atomic system representing the manifold of excitonic and biexcitonic states of the quantum dot and show that quantitative agreement is obtained only by including the interaction with LA-phonons in the solid state environment. Finally, we demonstrate the formation of dressed states emerging from a two-photon interaction between the artificial atom and the excitation field. The non-linear optical dressing induces a mixing of all four excitonic states that facilitates the tuning of the polarization selection rules of the artificial atom.