The recent detection of a nanohertz gravitational wave (GW) signal by Pulsar Timing Arrays (PTAs) offers the first evidence for a stochastic GW background (GWB) likely generated by a cosmological population of inspiralling supermassive black hole binaries (SMBHBs). Interestingly, the observed spectrum appears flatter than the canonical power law expected from circular, GW–driven binaries. This deviation may be caused by significant orbital eccentricities, possibly arising from complex dynamical interactions during binary formation and hardening. To investigate the origin and evolution of these eccentricities, we study how SMBHBs form and evolve, combining large-scale cosmological simulations, parsec-resolution N-body modelling, and semi-analytical evolution to trace them from galaxy mergers to GW emission in the PTA band. Starting from major mergers identified in the IllustrisTNG100-1 simulation, we perform targeted re-simulations using the Fast Multipole Method code Griffin to capture binary formation within realistic galactic environments. We find that galaxy encounters are typically highly eccentric, producing SMBHBs that retain substantial eccentricities until the GW-dominated regime. Moreover, these binaries tend to merge within a Hubble time, making them observable PTA sources. By specifically targeting multi-merger trees, we also assess the impact of previous mergers on the subsequent evolution of SMBHBs and study the formation and evolution of triple black hole systems. Triple interactions — frequently mediated by Kozai–Lidov oscillations — can further drive systems to extreme eccentricities, causing burst-like GW emission in the PTA band. This thesis develops a self-consistent theoretical framework linking the nanohertz GW background to the dynamical pathways of SMBHBs and triples, offering new insight into how these systems form, evolve, and potentially shape the low-frequency GW signal, now accessible by PTAs. ​