  We present the effective-field theory (EFT)-based cosmological full-shape
analysis of the anisotropic power spectrum of eBOSS quasars at the effective
redshift $z_{\rm eff}=1.48$. We perform extensive tests of our pipeline on
simulations, paying a particular attention to the modeling of observational
systematics, such as redshift smearing, fiber collisions, and the radial
integral constraint. Assuming the minimal $\Lambda$CDM model, and fixing the
primordial power spectrum tilt and the physical baryon density, we find the
Hubble constant $H_0=(66.7\pm 3.2)~$km~s$^{-1}$Mpc$^{-1}$, the matter density
fraction $\Omega_m=0.32\pm 0.03$, and the late-time mass fluctuation amplitude
$\sigma_8=0.95\pm 0.08$. These measurements are fully consistent with the
Planck cosmic microwave background results. Our eBOSS quasar $S_8$ posterior,
$0.98\pm0.11$, does not exhibit the so-called $S_8$ tension. Our work paves the
way for systematic full-shape analyses of quasar samples from future surveys
like DESI.
