Abstract.We report results from a comprehensive study of the nearby M dwarf Proxima Centauri with the XMM-Newton satellite, using simultaneously its X-ray detectors and the Optical Monitor with its U band filter. We find strongly variable coronal X-ray emission, with flares ranging over a factor of 100 in peak flux. The low-level emission is found to be continuously variable on at least three time scales (a slow decay of several hours, modulation on a time scale of 1 hr, and weak flares with time scales of a few minutes). Several weak flares are characteristically preceded by an optical burst, compatible with predictions from standard solar flare models. We propose that the U band bursts are proxies for the elusive stellar non-thermal hard X-ray bursts suggested from solar observations. In the course of the observation, a very large X-ray flare started and was observed essentially in its entirety. Its peak luminosity reached 3.9 × 10 28 erg s −1 [0.15-10 keV], and the total X-ray energy released in the same band is derived to be 1.5 × 10 32 ergs. This flare has for the first time allowed to measure significant density variations across several phases of the flare from X-ray spectroscopy of the O He-like triplet; we find peak densities reaching up to 4 × 10 11 cm −3 for plasma of about 1-5 MK. Abundance ratios show little variability in time, with a tendency of elements with a high first ionization potential to be overabundant relative to solar photospheric values. Using Fe lines with different oscillator strengths, we do not find significant effects due to opacity during the flare, indicating that large opacity increases are not the rule even in extreme flares. We model the large flare in terms of an analytic 2-Ribbon flare model and find that the flaring loop system should have large characteristic sizes (≈1R * ) within the framework of this simplistic model. These results are supported by full hydrodynamic simulations. Comparing the large flare to flares of similar size occurring much more frequently on more active stars, we propose that the X-ray properties of active stars are a consequence of superimposed flares such as the example analyzed in this paper. Since larger flares produce hotter plasma, such a model also explains why, during episodes of low-level emission, more active stars show hotter plasma than less active stars.