Here is a list of books for those wishing to dig deeper:
1) The Information by Gleick is a book covering everything from biographies of the key historical figures and contributors to contemporary applications of information theory in quantum mechanics.
2) Elements of Information Theory by Joy Thomas and Thomas Cover is a thorough and engaging textbook.
3) Quantum information and quantum computation by Nielsen and Chuang explaining both classical and quantum information with some practical examples.
4) Entropy and Information by Volkenstein a Soviet popular science book with math-heavy examples from biology, chemistry and physics
and as an aside I can also recommend "Willful Ignorance: The Mismeasure of Uncertainty" by Weisberg, which is an engaging history review of probability theory and its key inventors
> 2) Elements of Information Theory by Joy Thomas and Thomas Cover is a thorough and engaging textbook.
Thomas & Cover is THE textbook on information theory -- no doubt -- but you and I have very different definitions of engaging.
For a different kind of engaging, I would recommend Dave MacKay's "Information Theory, Inference, and Learning Algorithms", which can be found on his website:
1) The Information by Gleick is a book covering everything from biographies of the key historical figures and contributors to contemporary applications of information theory in quantum mechanics.
2) Elements of Information Theory by Joy Thomas and Thomas Cover is a thorough and engaging textbook.
3) Quantum information and quantum computation by Nielsen and Chuang explaining both classical and quantum information with some practical examples.
4) Entropy and Information by Volkenstein a Soviet popular science book with math-heavy examples from biology, chemistry and physics
and as an aside I can also recommend "Willful Ignorance: The Mismeasure of Uncertainty" by Weisberg, which is an engaging history review of probability theory and its key inventors