The allowed charge-changing transitions are considered to be the most general weak processes of spin-isospin ( ) form that play a crucial role in several nuclear processes. Equally important is their contribution in astrophysics, particularly in nuclear synthesis and supernovaexplosions. As per previous simulation results, weak interaction rates on fp shell nuclide are considered intensely signi cant for supernova physics. These transitions have significant in uence on the stellar core vis- a-vis controlling the lepton content (Ye) of stellar matter throughout the silicon shell burning stages of massive stars to the presupernova and core-collapse stages. Simulation of stellar events require Gamow-Teller (GT) strength distributions, preferably for hundreds of nuclei. Because of scarcity of experimental data, one is compelled to calculate GT strength distributions using microscopic theoretical nuclear models. The knowledge of measured GT strength should be broadened and theoretical attempts should be done to reproduce them and the charge-changing transitions of nuclei that are present far away from the stability line should be calculated. Therst-forbidden (FF) transition becomes important, in the circumstances where allowed charge-changing transitions are not favored, speci cally for neutron-rich (heavier) nuclide due to phase space considerations. In this thesis the deformed proton-neutron quasi-particle random phase approximation (pn- QRPA) theory was applied in stellar environment, for the investigation of allowed GT and uniquerst-forbidden (U1F) transitions (j Jj = 2) strength for a number of astrophysical important (medium heavy and heavy) nuclei. The calculated terrestrial beta-decay halflives (T1=2) values were compared with previous theoretical work and experimental results where it was concluded that the deformed pn-QRPA calculation are in decent comparison with measured data. The agreement of the calculated T1=2 values with the experimental data provide an idea about the correctness of the calculated weak-rates. The stellar weak interaction rates (GT and U1F) were computed over broad range of stellar temperature (0.01 GK { 30 GK) and density (10 { 1011 g/cm3) domain for astrophysical applications. viii We have compared the calculated weak-rates with previous other theoretical models compilations (wherever possible). Di erences were noticed with these previous models results and their impacts on the presupernova mechanism and for core-collapse supernova were discussed. In a recent study by Cole et al. [A. L. Cole, et al., Phys. Rev. C 86, 015809 (2012)], it was concluded that QRPA calculations show larger deviations and overestimate the total experimental GT strength. It was also concluded that QRPA calculated electron capture rates exhibit larger deviation than those derived from the measured charge-changing transitions strength. This work has probed the conclusion of the Cole et al. study and provides useful information on the performance of QRPA-based models. Ourndings showed that this is not the case for all type of QRPA models. In this work we did not assume Brink- Axel hypothesis as considered in previous shell models calculation. This made the current calculation unique and fully microscopic in nature. It is hoped that these microscopic compilations of stellar rates (allowed GT and U1F) will demonstrate enormous signi cance for core-collapse simulator worldwide. Our study suggests that the addition of rank (0 and 1) operators in FF transitions can further improve the comparison which remains unattended in this work.