The layered perovskite oxide Sr 2RuO 4 appears to be an ideal material to investigate unconventional superconductivity in real depth. We have performed a de Haas–van Alphen (dHvA) study in this material in fields up to 33 T and temperatures down to 30 mK. The results indicate that the Fermi liquid description of the normal state remains valid up to the highest fields, with unchanged mass renormalization and linear spin susceptibility. In a quantum critical point scenario of superconductivity, this would indicate that the corresponding order parameter only couples weakly to a magnetic field. We were also able, for the first time, to directly observe a beat in the dHvA oscillations corresponding to the γ-surface which is the largest and thermodynamically most important Fermi surface sheet. This complements and further extends the Fermi surface description presented elsewhere.