Explore the intricate connections between entanglement entropy, quantum field theory, and holography in this comprehensive lecture. Delve into the fundamental concepts of classical and quantum information theory, including subsystems, entanglement measures, and mutual information. Examine the application of these principles to quantum field theory and spin systems, with a focus on entropy and entanglement in extended systems. Gain insights into the mathematical foundations and physical implications of entanglement, from basic inequalities to advanced estimates. Conclude with a Q&A session to further clarify complex topics and their relevance to modern physics research.