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The physical motivations and performance of the TAIGA (Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy) project are presented. The TAIGA observatory addresses ground-based gamma-ray astronomy and astroparticle physics at energies from a few TeV to several PeV, as well as cosmic ray physics from 100 TeV to several EeV. The pilot TAIGA complex is located in the Tunka valley, $\sim$50 km West from the southern tip of the lake Baikal. It includes the air Cherenkov light integrating TAIGA-HiSCORE array with 120 wide angle optical stations distributed over on area of $\sim$1 km2and three 4-m class Imaging Atmospheric Cherenkov Telescopes of the TAIGA-IACT array. The latter array has a shape of a triangle with side lengths of about 300m, 400m and 500m. The expected integral sensitivity of the 1 km2 TAIGA detector will be about 2,5 × 10-13 TeV cm-2sec-1for detection of E ≥ 100 TeV gamma-rays in 300 hours of observations. The combination of the wide angle Cherenkov array with IACTs offers a cost-effective way to build a really large (up to 10 km2) array for very high energy gamma-ray astronomy. The reconstruction of the given EAS energy, incoming direction and the core position, from the TAIGA-HiSCORE data, allows one to increase the distance between the relatively expensive IACTs of to 600-800 m. These, together with the surface and underground electron/muon detectors will be used for selection of gamma-ray induced EAS.Present status of the project, together with the current array description and the first experimental results and plans for the future are presented.