In this series of lectures, I plan to give an overview to various quantum information concepts and their application in quantum many-body physics. I plan to talk about the following topics:

1. Fundamentals of quantum information theory. I will start from classical information theory concepts such as Shannon entropy and relative entropy, and discuss their quantum generalization. I will discuss important quantum information concepts such as quantum channel, quantum measurements and quantum error correction.

2. Quantum entanglement in many-body systems. I will discuss different physical systems for which quantum entanglement has been studied, including free bosons and free fermions, stabilizer code states, random states and random tensor network states. I may also discuss other related topics such as many-body localization, thermalization, etc.

3. Quantum information and quantum gravity. I will give an overview of holographic duality and its relation to quantum information concepts, including the Ryu-Takayanagi formula that relates entanglement entropy with area, entanglement wedge and quantum error correction code, out-of-time-order correlation, etc.

These lectures are meant to be informal and do not plan to systematically cover all topics in these fields.