Quantum phenomena provide computing and information handling paradigms that are distinctly different and arguably much more powerful than their classical counterparts. In the past quarter of the century, much progress has been made on the theoretical side. Experiments have been carried out in which quantum computational operations are executed on a small number of quantum bits. The NSF has declared this general area one of the ten big ideas for future investments. In June 2018, the science committee of the House of Representatives unanimously approved the National Quantum Initiative Act (H.R.~6227), which has created a 10-year federal effort to boost quantum science. Similar funding commitments have been made throughout the world. This course provides an introduction to the theory of quantum computing and information. The covered topics include 1) the fundamental elements of quantum information processing (qubits, unitary transformations, density matrices, measurements), 2) entanglement based communications protocols (e.g., teleportation) and games (e.g., CHSH), the Bell inequalities, 3) quantum algorithms such as Shor's factoring and Grover's search, and 4) basic (quantum) error correction algorithms. The course material is accessible to undergraduate and graduate students with a variety of backgrounds, e.g., electrical engineers, physicists, mathematicians, and computer scientists