We report a comprehensive study of magneto-oscillatory phenomena in the normal state of Sr2RuO4, the first layered perovskite superconductor (T-c congruent to 1 K) not based on copper. The form of the quasiparticle spectrum observed may be interpreted in terms of an almost two-dimensional Fermi liquid model which is consistent with Luttinger's theorem and successfully predicts bulk thermodynamic and transport properties at low temperatures. A study of the spectra and transport along the c axis provides insights into the different normal state and superconducting behavior of Sr2RuO4 and the cuprates.