IXPE, the Imaging X-ray Polarimetry Explorer, has been selected as a NASA SMEX mission to be flown in 2021. It will perform polarimetry resolved in energy, in time and in angle as a break-through in High Energy Astrophysics. IXPE promises to ’re-open’, after 40 years, a window in X-ray astronomy adding two more observables to the usual ones. It will directly measure the geometrical parameters of many different classes of sources eventually breaking possible degeneracies. The probed angular scales (30”) are capable of producing the first X-ray polarization maps of extended objects with scientifically relevant sensitivity. This will permit mapping the magnetic fields in Pulsar Wind Nebulae and Super-Nova Remnants at the acceleration sites of 10-100 TeV electrons. Additionally, it will probe vacuum birefringence effects in systems with magnetic fields far larger than those reachable with experiments on Earth. The payload of IXPE consists of three identical telescopes with mirrors provided by MSFC/NASA. The focal plane is provided by ASI with IAPS/INAF responsible for the overall instrument that includes detector units that are provided by INFN. ASI also provides, in kind, the Malindi Ground Station. LASP is responsible for the Mission Operation Center while the Science Operation Center is at MSFC. The operations phase lasts at least two years. All the data including those related to polarization will be made available quickly to the general user. In this paper we present the mission, its payload and we discuss a few examples of astrophysical targets.