The physics motivations and advantages of the new TAIGA (Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy) detector are presented. TAIGA aims at gamma-ray astronomy at energies from a few TeV to several PeV, as well as cosmic ray physics from 100 TeV to several EeV. For the energy range 30 – 200 TeV the sensitivity of 10 km2 area TAIGA array for the detection of local sources is expected to be 5 × 10¯¹⁴ erg cm¯² sec¯¹ for 300 h of observations. Reconstruction of the given EAS energy, incoming direction and its core position, based on the timing TAIGA-HiSCORE data, allows one to increase a distance between the IACTs up to 600-1000 m. The low investments together with the high sensitivity for energies ≥ 30-50 TeV make this pioneering technique very attractive for exploring the galactic PeVatrons and cosmic rays. At present the TAIGA first stage has been constructed in Tunka valley, 50 km West from the Lake Baikal. The first experimental results of the TAIGA first stage are presented.