The low-energy electronic structure, including the Fermi surface topology, of the itinerant metamagnet Sr$_{4}$Ru$_{3}$O$_{10}$ is investigated for the first time by synchrotron-based angle-resolved photoemission. Well-defined quasiparticle band dispersions with matrix element dependencies on photon energy or photon polarization are presented. Four bands crossing the Fermi-level, giving rise to four Fermi surface sheets are resolved; and their complete topography, effective mass as well as their electron and hole character are determined. These data reveal the presence of kink structures in the near-Fermi-level band dispersion, with energies ranging from 30 meV to 69 meV. Together with previously reported Raman spectroscopy and lattice dynamic calculation studies, the data suggest that these kinks originate from strong electron-phonon coupling present in Sr$_{4}$Ru$_{3}$O$_{10}$. Considering that the kink structures of Sr$_{4}$Ru$_{3}$O$_{10}$ are similar to those of the other three members of the Ruddlesden Popper structured ruthenates, the possible universality of strong coupling of electrons to oxygen-related phonons in Sr$_{n+1}$Ru$_{n}$O$_{3n+1}$ compounds is proposed.
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