Lectures are devoted to X-ray radiation arising from the interaction of a laser with matter, and how it is used to diagnose plasma parameters. X-rays have many advantages over radiation in the optical and VUV-photon ranges. These are a prompt (on the fs-scale) relaxation of excited ion states (compare with the ns-scale for optical and tens of ps- for VUV photons), low plasma absorption, and simple interpretation of the measured spectra. Plasma generated in short-pulse laser interaction with matter has transient (time-dependent) features. It will be shown that the laser-produced plasmas are far from the thermodynamic equilibrium and have strong deviations from the Saha-Boltzmann distribution of bound electrons and from the Maxwell distribution of free electrons. All this must be taken into account in order not to be mistaken in the interpretation of experimental data. In the lectures, particular attention is paid to the discussion of the formation and application of K-alpha and He-alpha lines widely used for diagnostics of short pulse laser-matter interaction.