Spiral galaxies confront us with many questions. Two of them are the origin of the spiral structures in these galaxies and why these galaxies rotate in their outer parts much faster than expected. In my talk I give new answers to both questions. The key hereby are stationary solutions of the flat Vlasov-Poisson system which resemble spiral galaxies very well. Such galaxies are difficult to model because the mass in spiral galaxies is moving on almost circular orbits around the galactic center. This 'almost' makes things difficult; how to implement it in a self-consistent model? But we cannot ignore it because it is necessary for stability. I solved this mathematical problem and this enables us to shed a new light on the physical questions mentioned above. Dark Matter will play no role in our answers; it is even important that we omit it.