  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.
