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The relativistic quantum string quark model, proposed earlier, is applied toall mesons, from pion to $\Upsilon$, lying on the leading Regge trajectories(i.e., to the lowest radial excitations in terms of the potential quarkmodels). The model describes the meson mass spectrum, and comparison withmeasured meson masses allows one to determine the parameters of the model:current quark masses, universal string tension, and phenomenological constantsdescribing nonstring short-range interaction. The meson Regge trajectories arein general nonlinear; practically linear are only trajectories for light-quarkmesons with non-zero lowest spins. The model predicts masses of many newhigher-spin mesons. A new $K^*(1^-)$ meson is predicted with mass 1910 Mev. Insome cases the masses of new low-spin mesons are predicted by extrapolation ofthe phenomenological short-range parameters in the quark masses. In this waythe model predicts the mass of $\eta_b(1S)(0^{-+})$ to be $9500\pm 30$ MeV, andthe mass of $B_c(0^-)$ to be $6400\pm 30$ MeV (the potential model predictionsare 100 Mev lower). The relativistic wave functions of the composite mesonsallow one to calculate the energy and spin structure of mesons. The averagequark-spin projections in polarized $\rho$-meson are twice as small as thenonrelativistic quark model predictions. The spin structure of $K^*$ reveals an80% violation of the flavour SU(3). These results may be relevant tounderstanding the ``spin crises'' for nucleons.Comment: 30 pages, REVTEX, 6 table

Masses and internal structure of mesons in the string quark model