  The importance of electronic correlation effects in the layered perovskite
Sr$_2$RuO$_4$ is evidenced. To this end we use state-of-the-art LDA+DMFT (Local
Density Approximation + Dynamical Mean-Field Theory) in the basis of Wannier
functions to compute spectral functions and the quasiparticle dispersion of
Sr$_2$RuO$_4$. The spectra are found to be in good agreement with various
spectroscopic experiments. We also calculate the $\textbf{k}$-dependence of the
quasiparticle bands and compare the results with new angle resolved
photoemission (ARPES) data. Two typical manifestations of strong Coulomb
correlations are revealed: (i) the calculated quasiparticle mass enhancement of
$m^*/m \approx2.5$ agrees with various experimental results, and (ii) the
satellite structure at about 3 eV binding energy observed in photoemission
experiments is shown to be the lower Hubbard band. For these reasons
Sr$_2$RuO$_4$ is identified as a strongly correlated 4$d$ electron material.
