The physics motivations and advantages of the hybrid detector complex TAIGA are presented. TAIGA aims to address gamma-ray astronomy at energies from a few TeV to several PeV units, as well as cosmic-ray physics from 100 TeV to several EeV units and astroparticle physics problems. In 2021 deployment and commissioning of the one square kilometer TAIGA setup in the Tunka valley ∼ 50 km West from Lake Baikal will be finished. The first experimental results with the TAIGA are presented.