The Pierre Auger Observatory, located on a vast, high plain in western Argentina, is the world's largest cosmic ray observatory. The objectives of the Observatory are to probe the origin and characteristics of cosmic rays above $10^{17}$ eV and to study the interactions of these, the most energetic particles observed in nature. The Auger design features an array of 1660 water-Cherenkov particle detector stations spread over 3000 km$^2$ overlooked by 24 air fluorescence telescopes. In addition, three high elevation fluorescence telescopes overlook a 23.5 km$^2$, 61-detector infilled array with 750 m spacing. The Observatory has been in successful operation since completion in 2008 and has recorded data from an exposure exceeding 40,000 km$^2$ sr yr. This paper describes the design and performance of the detectors, related subsystems and infrastructure that make up the Auger Observatory.