  The single-layered ruthenate Sr$_2$RuO$_4$ has attracted a great deal of
interest as a spin-triplet superconductor with an order parameter that may
potentially break time reversal invariance and host half-quantized vortices
with Majorana zero modes. While the actual nature of the superconducting state
is still a matter of controversy, it has long been believed that it condenses
from a metallic state that is well described by a conventional Fermi liquid. In
this work we use a combination of Fourier transform scanning tunneling
spectroscopy (FT-STS) and momentum resolved electron energy loss spectroscopy
(M-EELS) to probe interaction effects in the normal state of Sr$_2$RuO$_4$. Our
high-resolution FT-STS data show signatures of the \beta-band with a distinctly
quasi-one-dimensional (1D) character. The band dispersion reveals surprisingly
strong interaction effects that dramatically renormalize the Fermi velocity,
suggesting that the normal state of Sr$_2$RuO$_4$ is that of a 'correlated
metal' where correlations are strengthened by the quasi 1D nature of the bands.
In addition, kinks at energies of approximately 10meV, 38meV and 70meV are
observed. By comparing STM and M-EELS data we show that the two higher energy
features arise from coupling with collective modes. The strong correlation
effects and the kinks in the quasi 1D bands may provide important information
for understanding the superconducting state. This work opens up a unique
approach to revealing the superconducting order parameter in this compound.
