Explore the intricacies of quantum extremal surface prescription and its leading order corrections in this comprehensive lecture. Delve into paradoxes, examine the dust bowl example, and investigate evaporating black holes. Gain insights into smooth max entropy, the replica trick, and fixed area states. Analyze refinement techniques, semiclassical states, and entanglement reconstruction. Conclude with an examination of one-shot state merging, providing a thorough understanding of advanced concepts in quantum physics and information theory.