A bimodality has been seen in the morphology, colour and star-forming properties of galaxies. Throughout cosmic time, the number of galaxies that are quenched to join the red-sequence has increased, unlike the number of star forming galaxies. Post-starburst galaxies (PSB) are suspected to be a transition phase between these two stages. We tried to answer the questions of the mechanism for this transformation. The goal of our work is to see whether or not all PSB in the nearby universe are being quenched to join the red-sequence and by which mechanism. We try to show if there is any difference between the low and high redshift PSB with regard to the accumulated stellar mass in the last 1 and 1.5 Gyr, the star formation history and the amount of dust within the galaxies. In this work we fit the observed galaxies with the new STARLIGHT code that can fit spectra with or without photometric data with a library of synthetic models. First we investigate 189 PSB candidates in the low redshift Sloan Digital Sky Survey (SDSS) and 1877 comparison samples of star forming and passive galaxies. Depending on the mass, low or high, we found more than one pathway and mechanism that may transform the blue cloud to become red sequence type galaxies. Secondly we use Ultra Deep Survey (UDS) and the spectroscopic follow-up of the UKIDSS Ultra-Deep Survey (UDSz) data for the PSB galaxies at 0.9 ≤ z ≤ 1.2. From the fitting of 323 galaxies, we determine more constrained physical properties of UDSz high redshift galaxies, such as the star formation history, mass fraction that formed at the time of the burst and the dust contents of the galaxies. We speculate that a higher gas content in these galaxies could have led to the higher burst. "I offer my gratitude to both the Ministry of Higher Education and Scientific Research (MOHESR) and the University of Babylon in my beloved country Iraq for their financial support." -- Acknowledgements