The Imaging X-ray Polarimetry Explorer (IXPE) will expand the information space for study of cosmic sources, by adding polarization to the properties (time, energy, and position) observed in x-ray astronomy. Selected in 2017 January as a NASA Astrophysics Small Explorer (SMEX) mission, IXPE will be launched into an equatorial orbit in 2021. The IXPE observatory includes three identical x-ray telescopes, each comprising a 4-m-focal-length (grazing-incidence) mirror module assembly (MMA) and a polarization-sensitive (imaging) detector unit (DU). The optical bench separating the MMAs from the DUs is a deployable boom with a tip/tilt/rotation stage for DU-to-MMA (gang) alignment, similar to the configuration used for the NuSTAR observatory. The IXPE mission will provide scientifically meaningful measurements of the x-ray polarization of a few dozen sources in the 2-8 keV band, over the first two years of the mission. For several bright, extended x-ray sources (pulsar wind nebulae, supernova remnants, and an active-galaxy jet), IXPE observations will produce polarization maps indicating the magnetic structure of the synchrotron emitting regions. For many bright pulsating x-ray sources (isolated pulsars, accreting x-ray pulsars, and magnetars), IXPE observations will produce phase-resolved profiles of the polarization degree and position angle.