The nuclear and magnetic structure and full magnon dispersions of yttrium iron garnet Y3Fe5O12 have been studied using neutron scattering. The refined nuclear structure is distorted to a trigonal space group of R3̄. The highest-energy dispersion extends up to 86 meV. The observed dispersions are reproduced by a simple model with three nearest-neighbor-exchange integrals between 16a (octahedral) and 24d (tetrahedral) sites, Jaa, Jad, and Jdd, which are estimated to be 0.00±0.05, -2.90±0.07, and -0.35±0.08 meV, respectively. The lowest-energy dispersion below 14 meV exhibits a quadratic dispersion as expected from ferromagnetic magnons. The imaginary part of q-integrated dynamical spin susceptibility χ″(E) exhibits a square-root energy dependence at low energies. The magnon density of state is estimated from χ″(E) obtained on an absolute scale. The value is consistent with the single chirality mode for the magnon branch expected theoretically.