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 eclipses1 and from space at distances as small as 0.3 astronomical units2-5 to the Sun. Previous observations6-8 of dust scattering have not confirmed the existence of the theoretically predicted dust-free zone near the Sun9-11. The transient nature of the corona has been well characterized for large events, but questions still remain (for example, about the initiation of the corona12 and the production of solar energetic particles13) and for small events even its structure is uncertain14. Here we report imaging of the solar corona15 during the first two perihelion passes (0.16-0.25 astronomical units) of the Parker Solar Probe spacecraft13, 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 zone9-11. 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 ropes12,16 and the predicted, but not yet observed, magnetic islands17,18 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 predicted19, streamers are composed of yet smaller substreamers channelling continual density fluctuations at all visible scales.