The Orbital Observatory Spektr-RG (SRG), equipped with the grazing-incidence X-ray telescopes Mikhail Pavlinsky ART-XC and eROSITA, was launched by Roscosmos to the Lagrange L2 point of the Sun-Earth system on Jule 13, 2019. The launch was carried out from the Baikonur cosmodrome by a Proton-M rocket with a DM-03 upper stage. The German telescope eROSITA was installed on SRG under an agreement between Roskosmos and the DLR German Aerospace Agency. In December 2019, the Observatory started to perform its main scientific task: scanning the celestial sphere in order to obtain maps of the entire sky in X-rays in several energy ranges (from 0.3 to 8 keV, eROSITA, and from 4 to 30 keV, ART-XC). By mid-December 2020, the second 6-month full-sky scan had been completed. Over a period of 4 years, it is planned to obtain 8 independent maps of the entire sky in each of the energy ranges. The sum of these maps will provide high sensitivity and reveal more than three million quasars and over one hundred thousand massive galaxy clusters and galaxy groups. The availability of 8 sky maps will enable monitoring of long-term variability (every six months) of a huge number of extragalactic and Galactic X-ray sources, including hundreds of thousands of stars with active coronae. In addition, the rotation of the satellite around the axis directed toward the Sun with a period of 4 hours makes it possible to track faster variability of bright X-ray sources during one day every half a year. The chosen strategy of scanning the sky leads to the formation of deep survey zones near both ecliptic poles. The paper presents sky maps obtained by the telescopes aboard SRG during the first scan of the entire sky and a number of results of deep observations performed during the flight to the L2 point in the frame of the Performance Verification program, demonstrating the capabilities of the Observatory in imaging, spectroscopy and timing of X-ray sources. It is planned that in December 2023 the Observatory will switch, for at least two years, to observations of the most interesting sources in the sky in triaxial orientation mode and deep scanning of selected celestial fields with an area of up to 150 square degrees. These modes of operation were tested during the Performance Verification phase. Every day, data from the SRG observatory are dumped onto the largest antennae of the Russian Deep Space Network in Bear Lakes and near Ussuriysk.