We report results of deep X-ray observations of AB Doradus obtained with the XMM-Newton observatory during its Performance Verification phase. The main objective of the analysis is a study of the spectral variability of coronal plasma in a very active star, including investigations of the variable thermal structure, abundance variations, and possible density changes during flares. AB Dor revealed both quiescent and flaring emission. The RGS spectra show flux changes in lines of highly ionized Fe during the flares, and an increase of the continuum. Elemental abundances increase in the early flare phases, by a factor of three. The quiescent abundances are lower than corresponding solar photospheric values, and tend to increase with increasing first ionization potential, contrary to the behavior in the solar corona. High-resolution spectra show an average density of the cool plasma of ≈3 10^10 cm−3; this value does not change during the flares. We analyse and model the temporal behavior of heating and cooling, and present model results for one of the flares. We find that magnetic loops with a semilength of the order of 2.5 10^10 cm ≈ 0.3 R* are involved. ; M. A. acknowledges support from the Swiss National Science Foundation (grants 2100-049343 and 2000-058827), from the Swiss Academy of Sciences, and from the Swiss Commission for Space Research. H. M., K. B, and J. P. acknowledge financial support from PPARC. A. M. and R. P. acknowledge support from the Italian Space Agency. SRON is supported financially by NWO. ; Peer-reviewed ; Publisher Version