We report the properties of cosmic ray nuclei from protons to nickel (Z=1–14, 16, 26, and 28) in the rigidity range from 2 GV to 3 TV collected by the Alpha Magnetic Spectrometer on the International Space Station from May 19, 2011 to May 6, 2021. We found that the primary cosmic rays He-C-O-Fe-Ni, and Ne-Mg-Si-S belong to two different classes of cosmic rays. We also found that the secondary cosmic rays Li-Be-B and F belong to another two different classes of cosmic rays.The rigidity dependences of the secondary cosmic rays and the primary cosmic rays are distinctly different. In particular, above ∼ 200 GV the secondary cosmic rays harden twice as much as the primary cosmic rays. The third group of cosmic rays N, Na, and Al can be described as linear combinations of primary (O, Si) and secondary (B, F) cosmic rays. Compared with O and Si, the primary cosmic rays C, Ne, Mg, and S were found to have secondary component, similar to N, Na, and Al. As a result, the C/O, N/O, Ne/Si, Na/Si, Al/Si, Mg/Si, and S/Si abundance ratios at the source are directly determined independent of cosmic ray propagation. Finally, we found that the lightest and most abundant primary proton cosmic rays have two components, the first being with the same rigidity dependence as He-C-O-Fe-Ni and the second with rigidity spectral index softer than the first one by Δ𝑝/𝐻𝑒 = 0.30 ± 0.01.