The major aim of experimental nuclear physics is to extract structure information of nuclei as well as to understand the nature of the complex nuclear potential while the aim of nuclear astrophysics research is to understand the origin of the elements in the universe and to explain the energy production. Here, in the present research proposal, I have planned to study two astrophysically important nuclei ²⁶Al and ⁸Be. The nucleus ²⁶Al will be studied using single neutron transfer reaction ²⁷Al(⁶Li, ⁷Li)²⁶Al while the nucleus ⁸Be will be studied using the reactions ⁹Be(¹⁶O, ¹⁷O)⁸Be and ⁹Be(¹⁴N, ¹⁵N)⁸Be. The present study will be a completely new study because it has not been performed ever using the proposed nuclear reactions. The main aim of the present proposal is to extract important structure information like excitation energy, spin, parity, orbital and total angular momentum, and spectroscopic factor about the structure of the excited states of the nuclei ²⁶Al and ⁸Be. Spectroscopic factors will provide us information about the degree to which a state of nuclei ²⁶Al and ⁸Be populated through the above transfer reactions is a pure single-particle state or a mixture of single-particle levels. It is well known that spectroscopic factor is a fundamental property of nuclei and should be independent of involved reactions as well as energies; however, it has been observed that it does not always remain constant and may differ for different reaction probes used to study the nuclei of interest. This discrepancy may arise because of the choice of the optical model potential parameters used in the transfer reaction analysis. To extract the above structure information using distorted wave Born approximation calculation requires suitable optical model potential parameters (OMP) and these parameters will be extracted from the elastic scattering data. Elastic scattering data will be measured simultaneously with transfer reaction data in the present study. Several sets of OMP will be extracted for each reaction at several energies to examine the dependence of OMP on the energy. The examination of the dependence of OMP on energy will be helpful to examine the consistency of the spectroscopic factors for the excited states of the nuclei ²⁶Al and ⁸Be. The parameters (like optical model potential parameter, Bound state parameters, Q-value spectroscopic factors, etc. ) extracted from the analysis of the above said transfer reactions will be utilized to extract the asymptotic normalization coefficient (ANC) and astrophysical S-factor from the nuclear astrophysics aspect of the present proposal. The results obtained from the present research proposal will be very useful to study the reaction rate calculation and energy production of stellar objects. Therefore, The present proposal is important from both the basic nuclear physics points of view as well as from nuclear astrophysics points of view.