The 2021 outburst of the symbiotic recurrent nova RS Oph was monitored with the Neutron Star Interior Composition Explorer Mission (NICER) in the 0.2–12 keV range from day one after the optical maximum, until day 88, producing an unprecedented, detailed view of the outburst development. The X-ray flux preceding the supersoft X-ray phase peaked almost 5 days after optical maximum and originated only in shocked ejecta for 21–25 days. The emission was thermal; in the first 5 days, only a non-collisional-ionization equilibrium model fits the spectrum, and a transition to equilibrium occurred between days 6 and 12. The ratio of peak X-ray flux measured in the NICER range to that measured with Fermi in the 60 MeV–500 GeV range was about 0.1, and the ratio to the peak flux measured with H.E.S.S. in the 250 GeV–2.5 TeV range was about 100. The central supersoft X-ray source (SSS), namely the shell hydrogen burning white dwarf (WD), became visible in the fourth week, initially with short flares. A huge increase in flux occurred on day 41, but the SSS flux remained variable. A quasi-periodic oscillation every ≃35 s was always observed during the SSS phase, with variations in amplitude and a period drift that appeared to decrease in the end. The SSS has characteristics of a WD of mass >1 M
⊙. Thermonuclear burning switched off shortly after day 75, earlier than in the 2006 outburst. We discuss implications for the nova physics.