SOFT X-ray observations are recognized as the best way to study the solar corona, as they are largely free of contaminating emission from other temperature regimes. They provide the only available method for seeing the corona on the disk, thereby avoiding the line-of-sight integration effects which are troublesome in limb observations. Here we present results from a high-resolution multilayer-coated X-ray imaging telescope, part of the Normal Incidence X-ray Telescope sounding rocket payload. From a flight at 16:35 UT on 11 September 1989 we obtained 40 images of the solar X-ray corona, with spatial resolution up to 0.75 arcsec. Images of the peak of a two-ribbon flare showed detailed structure within each ribbon, as well as the expected bright arches of emission connecting the ribbons. Active regions showed structure at a scale of 0.75 arcsec that was not visible in our 2-arcsec images taken during the same flight. The number of X-ray bright points1 is small, consistent with predictions based on the previous solar cycle2. The topology of the magnetic structure is complex and highly tangled, implying that the magnetic complexity of the photosphere is paralleled in the corona.