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
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:
It’s a fantastic explanation of the theory.
What passes for mundane obviousness today was once a strike of genius nobody else saw coming.
And that's part of what makes the paper so groundbreaking, too. Some things are groundbreaking in terms of explanatory power but don't make it into the fabric of society. What Shannon's paper did was essentially weave the fabric of the digitally powered society.
And it did it so successfully that you think of it as obvious banalities today.
If this seems obvious to you and not remarkable it is only because of hindsight, because his insights have been absorbed into the common culture.
It’s among my favourite textbooks: you can feel his enthusiasm and personality through the pages. The world is a poorer place without him around.
That's well put.
A "binary digit" is either a zero or a one. It's a specific value.
A "bit" is an amount of information: a container that can hold a binary digit.