The paper provides a derivation of holographic entanglement entropy for spherical entangling surfaces. The authors use conformal mapping to map the boundary CFT to a hyperbolic geometry, where the vacuum state is mapped to a thermal state. This transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. Using the AdS/CFT dictionary, they calculate this thermodynamic entropy as the horizon entropy of a topological black hole in AdS space. In even dimensions, they also show that the universal contribution to the entanglement entropy is given by the A-type trace anomaly for any CFT, without reference to holography. The paper discusses the entanglement entropy in flat space, thermal behavior in \(R \times H^{d-1}\), and entanglement entropy in a cylindrical background. It then applies these results to the AdS/CFT correspondence, demonstrating that the entanglement entropy can be calculated as the horizon entropy of a black hole in AdS space. The authors also provide a non-trivial confirmation of the Ryu-Takayanagi proposal for holographic entanglement entropy.The paper provides a derivation of holographic entanglement entropy for spherical entangling surfaces. The authors use conformal mapping to map the boundary CFT to a hyperbolic geometry, where the vacuum state is mapped to a thermal state. This transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. Using the AdS/CFT dictionary, they calculate this thermodynamic entropy as the horizon entropy of a topological black hole in AdS space. In even dimensions, they also show that the universal contribution to the entanglement entropy is given by the A-type trace anomaly for any CFT, without reference to holography. The paper discusses the entanglement entropy in flat space, thermal behavior in \(R \times H^{d-1}\), and entanglement entropy in a cylindrical background. It then applies these results to the AdS/CFT correspondence, demonstrating that the entanglement entropy can be calculated as the horizon entropy of a black hole in AdS space. The authors also provide a non-trivial confirmation of the Ryu-Takayanagi proposal for holographic entanglement entropy.