We apply a novel analysis of the field and angle dependence of the quantum-
oscillatory amplitudes in the unconventional superconductor Sr2RuO4 to map
its Fermi surface (FS) in unprecedented detail and to obtain previously ina
ccessible information on the band dispersion. The three quasi-2D FS sheets
not only exhibit very diverse magnitudes of warping, but also entirely diff
erent dominant warping symmetries. We use the data to reassess recent resul
ts on c-axis transport phenomena.