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 S-11 wave which has two poles in the energy region below 2 GeV. Eleven nucleon resonances are observed in their decay into peta. At medium energies we find evidence for a new resonance N(2070)D-15 with (M,Gamma)=(2068+/-22, 295+/-40) MeV. At gamma energies above 1.5 GeV, a strong peak in the forward direction develops, signaling the exchange of vector mesons in the t channel.