Total and differential cross sections for the reaction p(gamma, eta)p have been measured for photon energies in the range from 750 MeV to 3 GeV. The low-energy data are dominated by the S11 wave which has two poles in the energy region below 2 GeV. Eleven nucleon resonances are observed in their decay into p eta. At medium energies we find evidence for a new resonance N(2070)D15 with (mass, width) = (2068+-22, 295+-40) MeV. At photon energies above 1.5 GeV, a strong peak in forward direction develops, signalling the exchange of vector mesons in the t channel.