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A new realization of the International Celestial Reference Frame (ICRF) is presented based on the work achieved by a working group of the International Astronomical Union (IAU) mandated for this purpose. This new realization, referred to as ICRF3, is based on nearly 40 years of data acquired by very long baseline interferometry. The ICRF3 includes positions at 8.4 GHz for 4536 sources, supplemented with positions at 24 GHz for 824 sources and at 32 GHz for 678 sources, for a total of 4588 sources. A subset of 303 sources among these, uniformly distributed on the sky, are identified as "defining sources" and as such serve to define the axes of the frame. Source positions are reported for epoch 2015.0 and must be propagated for observations at other epochs for the most accurate needs, accounting for the acceleration toward the Galactic center, which results in a dipolar proper motion field of amplitude 0.0058 milliarcsecond/yr (mas/yr). The frame shows a median positional uncertainty of about 0.1 mas in right ascension and 0.2 mas in declination, with a noise floor of 0.03 mas in the individual source coordinates. A subset of 500 sources is found to have extremely accurate positions at 8.4 GHz, in the range of 0.03 to 0.06 mas. Comparing ICRF3 with the Gaia Celestial Reference Frame 2 in the optical domain, there is no evidence for deformations larger than 0.03 mas between the two frames. Significant positional offsets between the three ICRF3 frequencies are detected for about 5% of the sources. Moreover, a notable fraction (22%) of the sources shows optical and radio positions that are significantly offset. There are indications that these positional offsets may be the manifestation of extended source structures. This third realization of the ICRF was adopted by the IAU at its 30th General Assembly in August 2018 and replaced the previous realization, ICRF2, on January 1, 2019.