This book focuses on AdS₃/CFT₂, addressing different aspects of this correspondence in field theory and in gravity, including entanglement entropy, higher genus partition function, and conformal block. Holographic entanglement entropy is an important area in holographic and quantum information, which implies a deep relation between geometry and quantum entanglement. In this book, the authors use holographic entanglement entropy as a tool to investigate AdS₃/CFT₂. They study the entanglement entropy at high temperature in field theory and in holographics, and show that the results match each other in classical and one-loop order. In the AdS₃/CFT₂system, they examine in detail the correspondence, exploring the higher genus partition function, entanglement entropy in a general system and conformal block, and they find good correspondence in field theory and gravity. The result strongly supports AdS₃/CFT₂ correspondence. In addition, they develop several important techniques in 2d CFT and 3d gravity, which also offer inspiration for other fields.