The field of quantum information theory hardly existed ten years ago, as an area of research. Advances in recent years now make it possible to create a textbook. The book is intended for undergraduates, in physics, computer science and related fields, and requires only linear algebra. The book is structured into five parts: introduction to the basic structure of quantum mechanics; classical information theory; information carrying capacities of quantum channels; review of quantum cryptography; and, algorithms and error correcting schemes for quantum computers.