Ever since the publication of P. W. Anderson&rsquos paradigm-shifting insight into the absence of diffusion in a medium with the random disorder, there has been a continuous effort to study disordered lattices in search of delocalization-localization (DL) transition. For a long, it was known that a DL transition could exist in a lattice with random disorder and nearest-neighbor (NN) hopping only in three dimensions. In lower spatial dimensional lattices, especially in one-dimension (1D), electronic wave functions are known to be exponentially localized at any energy, even for an arbitrarily weak strength of the disorder potential. However, later it was pointed out that spin-orbit coupling could lead to a DL transition in lower dimensions, which has been proved numerically in two dimensions. On the other hand, it has been observed that long-range hopping can induce the delocalization of electronic eigenstates even in 1D, without the requirement of spin-orbit coupling. Interestingly, in contrast to a lattice with completely random potential, a quasiperiodic lattice with NN hopping amplitude can show DL transition even in 1D without a mobility edge. However, recently it has been demonstrated that mobility edge can exist in 1D quasiperiodic lattice provided a power law modifies the hopping. The effect of the spin-orbit coupling is relatively well studied in the case of lattices with random potential, while there are still open questions that are not addressed in the quasiperiodic lattice. Motivated by this, in this thesis, we have studied the effect of the spin-orbit interaction, especially the Rashba spin-orbit (RSO) interaction that consists of a spin-preserving and spin-flipping hopping processes, on the 1D quasiperiodic lattice with NN and power-law hopping. In the case of a quasiperiodic lattice with NN hopping, we have found that in the presence of both the hopping processes induced by the Rashba spin-orbit interaction, the self-dual structure of the original problem remains unaltered and the self-dual point coincides with the DL transition. In the quasiperiodic lattice with power-law hopping, the RSO interaction is found to break the eigenspectrum into multiple mobility/multifractal edges.