Understanding how diffuse molecular clouds at large scales (~10 pc) assemble mass into dense, star-forming cores at small scales (~ 0.1 pc) is crucial to building a holistic theory of star formation. While recent observations suggest that filaments play an important role in the mass assembly of dense cores, detailed gas kinematics studies are still lacking. My dissertation presents three innovative techniques that enable us to study star-forming filaments' complex gas kinematics in unprecedented detail: multi-component spectral fit, multi-dimensional filament identification, and membership assignment of velocity-coherent structures. Through these techniques, I analyzed star-forming filaments in the Perseus Molecular Cloud and unveiled unexpectedly complex velocity structures at scales where filaments are well resolved, to as low as the 0.01 pc scale. Moreover, the correlations I discovered between the various filament properties further suggest a scenario in which thermally supercritical filaments grow continuously via accretion from their surroundings while simultaneously forming cores through fragmentation along their lengths. / Graduate / 2022-01-08