A data compilation is given of 140 meson and baryon resonances. Using the principles of nuclear physics as a guide, we deduce a set of meson and baryon excitation levels (analogous to vibrational levels) and corresponding rotational bands. The excitations occur as «excitation towers» built on a set of fundamental ground states. The excitations follow accurate 70 MeV and 210 MeV interval relationships. All binding energies are small ((1 ÷ 3)%). The rotational bands have cutoffs imposed by the requirement that the periphery should not exceed the velocity of light. We define a hadron basis set consisting of the spinless mass quanta 1 ≡ 70 MeV and 3 ≡ 210 MeV and the fermion spinorS ≡ 327 MeV,J = 1/2ħ. 1 and 3 differ in their isotopic-spin rules. By forming combinations of 1, 3 andS (and their antistates), we can accurately reproduce the masses, spins, widths and principal decay modes of the 140 meson and baryon resonances. A dozen of these resonances were first predicted by this model and then, subsequently, verified in the published data. We can extend the model by giving 1, 3 andS specific geometries and (integral) charge states and, thereby, reproduce the measured magnetic moments and charge splittings. When we do this, the mass of the muon is shown as related to the hadronic basis set. The strangeness quantum number fits naturally into the isotopic-spin formalism. The model is used to unravel a number of experimental puzzles, including the splitting in the A2-meson, the occurrence of a spin-1 ABC resonance and the existence of (M, η′, δ−) and (H, π N , ϕ) as singleI=1 meson resonances. The model is also helpful in accounting for some striking relationships in meson lifetimes. A dynamical method for testing particle symmetries is proposed, and implications for other branches of physics are briefly discussed. See the «Note added in proof» for important new experimental results and for recent theoretical improvements.