Primary cosmic nuclei are fused in stars and accelerated in supernova remnants to later diffuse in the magnetic fields of the Galaxy. The Alpha Magnetic Spectrometer (AMS), operating on the International Space Station since 2011, has measured the fluxes of primary cosmic-ray nuclei with unprecedented precision over a wide rigidity range with detailed study of systematic errors. Using more than a decade of data, AMS has collected billions of nuclei from protons to iron, enabling detailed studies of the spectral features. The results show that none of the primary fluxes follow a simple power law: the proton spectrum hardens above 45 GV and differs significantly from helium, which in turn shares an identical rigidity dependence with carbon and oxygen above ~60 GV, all hardening around 200 GV. Heavier nuclei such as neon, magnesium, silicon, and sulphur display another distinct rigidity dependence above ~80 GV, different from the lighter group, while iron aligns with the light nuclei above the same rigidity. These observations provide new insights into cosmic-ray acceleration and propagation in the Galaxy.