Quantum information theory synthesizes three major themes: quantum physics, computer science, and information theory. At the core of information theory lies the classical work of Claude E. Shannon, which we review in this course. We then introduce quantum information sources, quantum operations, and quantum tomography, and study three problems related to classical Shannon's theorems and subsequent extension to quantum computing. These involve compressing quantum information, transmitting both classical and quantum information through noisy quantum channels, and quantifying, characterizing, transforming, and utilizing quantum entanglement.