Post-starburst galaxies are a rare class of objects with unusual spectroscopic characteristics. Previous studies have shown that the presence of strong Balmer absorption lines in the spectra of these galaxies are consistent with a recent bust of star formation; however, the cause of such events remains unclear. Their environment and disturbed morphology suggest that many of them are likely remnants of gas-rich mergers of galaxies with comparable masses and models of galaxy mergers support that claim; however, some studies disagree and the origin of these curious systems remains an open debate. Post-starburst galaxies are also often regarded as a plausible transition channel between the blue continuously star-forming and quiescent red galaxies, commonly observed in the local Universe. This is supported by models of merger- driven starbursts, which cause structural transformation of galaxies consistent with evolution towards the red population, and can ultimately lead to quenching of star formation in the merger remnant; however, observational evidence for this scenario remains elusive. In my study I aimed to place further constraints on the role of galaxy mergers in triggering starbursts in local galaxies and to investigate whether the post-starburst galaxies are indeed in transition between the star-forming and passive phases of galaxy evolution, by the analysis of the morphology and structure of galaxies with spectroscopic signatures of a recent starburst. An important difference between this work and many previous studies is the post-starburst sample selection. Traditionally, post-starburst galaxies are selected to have completely quenched their star-formation; here, I also considered those which show spectroscopic sign of residual star-formation, selected using a method introduced by Wild et al. (2007). I have also followed a different approach to quantifying the morphology of galaxies, by means of an automated method for detecting visual post-merger signatures in galaxies, introduced as a part of this work. My analysis suggests that major mergers play a significant role in inducing starbursts in local Universe, but their significance declines as a function of the stellar mass of the galaxies. I also found that post-starburst galaxies have different structural properties in the low- and high-mass regimes and concluded that they are likely to be transitioning between the blue and red galaxy populations through a multi-stage scenario where both major and minor mergers are at play.