Advances of plasma diagnostics with high-resolution spectroscopy of   stellar coronae
  X-ray emission from cool stars is an important tracer for stellar activity. The X-ray luminosity reflects different levels of activity and covers four orders of magnitude in stars of spectral types M-F. Low spectral resolution provided by X-ray observations of stellar coronae in the past allowed the determination of temperature distributions and elemental abundances making use of atomic databases (listing line emissivities and bremsstrahlung continuum for a given temperature structure). The new missions XMM-Newton and Chandra carry X-ray gratings providing sufficient spectral resolution to measure the fluxes of strategic emission lines. I describe the different approaches applicable to low-resolution and high-resolution spectra, especially focusing on the new grating spectra with X-ray lines. From only a few lines it is possible to determine plasma temperatures and associated densities, to check for any effects from resonant scattering, and to identify particular abundance anomalies. Line-based temperature- and density measurements represent only a fraction of the total plasma, but the pressure environment of different fractions can be probed simply by selection of specific lines. Selected results are presented covering all aspects of line-based analyses. 
J.-U. Ness (Rudolf Peierls Centre for Theoretical Physics, University   of Oxford)