We present the scientific motivation and conceptual design of the P. Auger Observatory. Two giant ground arrays of water Čerenkov tanks overlooked by fluorescence detectors will cover an area of 3000 km2 each. They will be build in the Southern and Northern hemisphere to provide full sky coverage. The total aperture of 14000 km2sr will allow to study all observable aspects of cosmic rays from below 10 EeV up to arbitrarily high energies with an unprecedented accuracy.

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