Astronomical Roentgen Telescope – X-ray Concentrator (ART-XC) is the hard X-ray instrument with grazing incidence imaging optics on board the Spektr-Roentgen-Gamma (SRG) observatory. The SRG observatory is the flagship astrophysical mission of the Russian Federal Space Program, which was successively launched into orbit around the second Lagrangian point (L2) of the Earth-Sun system with a Proton rocket from the Baikonur cosmodrome on 13 July 2019. The ART-XC telescope will provide the first ever true imaging all-sky survey performed with grazing incidence optics in the 4–30 keV energy band and will obtain the deepest and sharpest map of the sky in the energy range of 4–12 keV. Observations performed during the early calibration and performance verification phase as well as during the ongoing all-sky survey that started on 12 December 2019 have demonstrated that the in-flight characteristics of the ART-XC telescope are very close to expectations based on the results of ground calibrations. Upon completion of its four-year all-sky survey, ART-XC is expected to detect approximately 5000 sources (~3000 active galactic nuclei, including heavily obscured ones, several hundred clusters of galaxies, ~1000 cataclysmic variables and other Galactic sources), and to provide a high-quality map of the Galactic background emission in the 4–12 keV energy band. ART-XC is also well suited for discovering transient X-ray sources. In this paper, we describe the telescope, the results of its ground calibrations, the major aspects of the mission, the in-flight performance of ART-XC, and the first scientific results.