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eROSITA Science Book: Mapping the Structure of the Energetic Universe

eROSITA is the primary instrument on the Russian SRG mission. In the first four years of scientific operation after its launch, foreseen for 2014, it will perform a deep survey of the entire X-ray sky. In the soft X-ray band (0.5-2 keV), this will be about 20 times more sensitive than the ROSAT all sky survey, while in the hard band (2-10 keV) it will provide the first ever true imaging survey of the sky at those energies. Such a sensitive all-sky survey will revolutionize our view of the high-energy sky, and calls for major efforts in synergic, multi-wavelength wide area surveys in order to fully exploit the scientific potential of the X-ray data. The design-driving science of eROSITA is the detection of very large samples (~10^5 objects) of galaxy clusters out to redshifts z>1, in order to study the large scale structure in the Universe, test and characterize cosmological models including Dark Energy. eROSITA is also expected to yield a sample of around 3 millions Active Galactic Nuclei, including both obscured and un-obscured objects, providing a unique view of the evolution of supermassive black holes within the emerging cosmic structure. The survey will also provide new insights into a wide range of astrophysical phenomena, including accreting binaries, active stars and diffuse emission within the Galaxy, as well as solar system bodies that emit X-rays via the charge exchange process. Finally, such a deep imaging survey at high spectral resolution, with its scanning strategy sensitive to a range of variability timescales from tens of seconds to years, will undoubtedly open up a vast discovery space for the study of rare, unpredicted, or unpredictable high-energy astrophysical phenomena. In this living document we present a comprehensive description of the main scientific goals of the mission, with strong emphasis on the early survey phases.