In this thesis, we investigate the entanglement structure of the SSH model using tools from quantum information theory. Our goal is to establish a clear link between topological phase and entanglement properties, particularly in the presence of thermal fluctuations. To do so, we leverage the fact that the SSH model defines a free-fermionic system, whose thermal and ground states are examples ffermionic Gaussian states. This allows us to use correlation matrix methods to efficiently compute entanglement-related quantities such as the reduced density matrix, concurrence, Bell violation, and the Peres-Horodecki criterion.