In this project, we explore non-Hermitian topological systems, focusing on the asymmetric Su-Schrieffer-Heeger (SSH) model, a one-dimensional non-Hermitian system with dimerization, asymmetric hopping, and imaginary staggered potentials. Depending on parameter choices, the model can exhibit Hermitian, non-Hermitian, sublattice symmetric, and PT-symmetric behavior, providing a thorough view of different symmetry types and topological models. We investigate exceptional points as a phenomenon unique to non-Hermitian systems, and topological phase transitions based on bandgap closure and symmetry-breaking points. We study topological invariants as essential features of topological quantum systems, introducing two winding numbers to distinguish between the Hermitian and non-Hermitian SSH models with or without symmetries. We also propose a method to compute entanglement in non-Hermitian systems and explore how bulk-boundary correspondence needs modification, as the standard version doesn’t apply for non-Hermitian systems. We demonstrate how topological winding numbers in periodic systems correspond to singular values in systems with open boundaries. In the PT-symmetric case, we present a detailed phase diagram that has not been addressed in prior studies. We provide analytical solutions, supported by numerical calculations, for the eigenspectrum with both open and closed boundary conditions, as well as for the singular-value spectrum.