The low-energy electronic structure of the itinerant metamagnet Sr3Ru2O7 is investigated by angle-resolved photoemission and density-functional calculations. We find well-defined quasiparticle bands with resolution-limited linewidths and Fermi velocities up to an order of magnitude lower than in single layer Sr2RuO4. The complete topography, the cyclotron masses, and the orbital character of the Fermi surface are determined, in agreement with bulk sensitive de Haas-van Alphen measurements. An analysis of the dxy band dispersion reveals a complex density of states with van Hove singularities near the Fermi level, a situation which is favorable for magnetic instabilities.