Dark matter in galaxies: the dark matter particle mass is about 2 keV

13 pages, 4 figures. Based on Lectures by H J de V at NuMass 2013, Milano-Bicocca, Feb 2013; at Cosmic Frontiers, SLAC, March 2013 and by H J de V and N G S at the Chalonge Torino Colloquium 2013, Apr 2013Warm dark matter (WDM) means DM particles with mass m in the keV scale. For large scales, for structures beyond 100 kpc, WDM and CDM yield identical results which agree with observations. For intermediate scales, WDM gives the correct abundance of substructures. Inside galaxy cores, below 100 pc, N-body classical physics simulations are incorrect for WDM because at such scales quantum effects are important for WDM. Quantum calculations (Thomas-Fermi approach) provide galaxy cores, galaxy masses, velocity dispersions and density profiles in agreement with the observations. All evidences point to a dark matter particle mass around 2 keV. Baryons, which represent 16% of DM, are expected to give a correction to pure WDM results. The detection of the DM particle depends upon the particle physics model. Sterile neutrinos with keV scale mass (the main WDM candidate) can be detected in beta decay for Tritium and Renium and in the electron capture in Holmiun. The sterile neutrino decay into X rays can be detected observing DM dominated galaxies and through the distortion of the black-body CMB spectrum. The effective number of neutrinos, N_{eff} measured by WMAP9 and Planck satellites is compatible with two Majorana sterile neutrinos with mass much smaller than the electron mass. One of them can be a WDM sterile neutrino. So far, not a single valid objection arose against WDM