Tomographic and 3-D analyses for extended, emission-line objects are applied to long-slit ESO NTT + EMMI high-resolution spectra of the intriguing planetary nebula NGC 7009, covered at twelve position angles. We derive the gas expansion law, the diagnostics and ionic radial profiles, the distance and the central star parameters, the nebular photo-ionization model and the spatial recovery of the plasma structure and evolution. The Saturn Nebula (distance~1.4 kpc, age~6000 yr, ionized mass~0.18

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... ) consists of several interconnected components, characterized by different morphology, physical conditions, excitation and kinematics. The internal shell, the main shell, the streams and the ansae expand at V(exp)~4.0xR" km/s, the outer shell, the caps and the equatorial pseudo-ring at V(exp)~3.15xR" km/s, and the halo at V(exp)~10 km/s. We compare the radial distribution of the physical conditions and the line fluxes observed in the eight sub-systems with the theoretical profiles coming from the photo-ionization code CLOUDY, inferring that all the spectral characteristics of NGC 7009 are explainable in terms of photo-ionization by the central star, a hot (logT*~4.95) and luminous (log L*/Lo~3.70) 0.60--0.61 Mo post--AGB star in the hydrogen-shell nuclear burning phase. The 3--D shaping of the Saturn Nebula is discussed within an evolutionary scenario dominated by photo-ionization and supported by the fast stellar wind: it begins with the superwind ejection, passes through the neutral, transition phase (lasting ~ 3000 yr), the ionization start (occurred ~2000 yr ago), and the full ionization of the main shell (~1000 yr ago), at last reaching the present days: the whole nebula is optically thin to the UV stellar flux, except the caps and the ansae.