Remote observations of the solar photospheric light scattered by electrons (the K-corona) and dust (the F-corona or zodiacal light) have been made from the ground during eclipses(1) and from space at distances as small as 0.3 astronomical units(2-5) to the Sun. Previous observations(6-8) of dust scattering have not confirmed the existence of the theoretically predicted dust-free zone near the Sun(9-11). The transient nature of the corona has been well characterized for large events, but questions still remain (for example, about the initiation of the corona(12) and the production of solar energetic particles(13)) and for small events even its structure is uncertain(14). Here we report imaging of the solar corona(15) during the first two perihelion passes (0.16-0.25 astronomical units) of the Parker Solar Probe spacecraft(13), each lasting ten days. The view from these distances is qualitatively similar to the historical views from ground and space, but there are some notable differences. At short elongations, we observe a decrease in the intensity of the F-coronal intensity, which is suggestive of the long-sought dust free zone(9-11). We also resolve the fine-scale plasma structure of very small eruptions, which are frequently ejected from the Sun. These take two forms: the frequently observed magnetic flux ropes(12,16) and the predicted, but not yet observed, magnetic islands(17,18) arising from the tearing-mode instability in the current sheet. Our observations of the coronal streamer evolution confirm the large-scale topology of the solar corona, but also reveal that, as recently predicted(19), streamers are composed of yet smaller substreamers channelling continual density fluctuations at all visible scales.