X-ray polarimetry, sometimes alone, and sometimes coupled to spectral and temporal variability measurements and to imaging, allows a wealth of physical phenomena in astrophysics to be studied. X-ray polarimetry investigates the acceleration process, for example, including those typical of magnetic reconnection in solar flares, but also emission in the strong magnetic fields of neutron stars and white dwarfs. It detects scattering in asymmetric structures such as accretion disks and columns, and in the so-called molecular torus and ionization cones. In addition, it allows fundamental physics in regimes of gravity and of magnetic field intensity not accessible to experiments on the Earth to be probed. Finally, models that describe fundamental interactions (e.g. quantum gravity and the extension of the Standard Model) can be tested. We describe in this paper the X-ray Imaging Polarimetry Explorer (XIPE), proposed in June 2012 to the first ESA call for a small mission with a launch in 2017 but not selected. XIPE is composed of two out of the three existing JET-X telescopes with two Gas Pixel Detectors (GPD) filled with a He-DME mixture at their focus and two additional GPDs filled with pressurized Ar-DME facing the sun. The Minimum Detectable Polarization is 14 % at 1 mCrab in 10E5 s (2-10 keV) and 0.6 % for an X10 class flare. The Half Energy Width, measured at PANTER X-ray test facility (MPE, Germany) with JET-X optics is 24 arcsec. XIPE takes advantage of a low-earth equatorial orbit with Malindi as down-link station and of a Mission Operation Center (MOC) at INPE (Brazil).

49 pages, 14 figures, 6 tables. Paper published in Experimental Astronomy http://link.springer.com/journal/10686