Introduction to Information Theory I'm studying bioengineering but in conversations and reading I've found that a great background in information theory as it applies to probability, statistics, random process, causation and inference is really useful. Can someone recommend some textbooks that cover information theory not so much from a communications standpoint? 
Thanks! 
 A: There really isn't much on information theory that isn't done from a communications perspective because that's historically how the subject has grown up. 
At the intersection of information theory and biology you might try some of the following for a (gentle) broader general perspective on their interaction:
Avery, John. Information Theory and Evolution. 
Yockey, H. P. Information theory, evolution and the origin of life.
Loewenstein, W. R. (1999). The Touchstone of Life: Molecular Information, Cell Communication and the Foundations of Life. Oxford University Press.
Moving more toward the technical side of information theory and likely a more sophisticated place for you to start:
Schneider, Thomas D. (2008). Information Theory Primer. (Available for download at Schneider's NIH website)
Adami, C. (2004). Information theory in molecular biology. Physics of Life Reviews, 1(1), 3-22. doi:10.1016/j.plrev.2004.01.002
And then the paper that spawned it all (you should be able to easily find it online), and which is highly readable:
Shannon, C. E. (1948). The mathematical theory of communication. Bell Labs
It's certainly worthwhile to purchase the UofI published version of the book with Warren Weaver's (lengthy) introduction.
Then to cap it all off, and assuming you've got some reasonable background in probability theory, random variables, and stochastic processes (a semester course will typically be sufficient) you might finally try one of the standard engineering texts:
Cover, Thomas M. and Thomas, Joy A. Elements of Information Theory, 2nd Edition (Wiley Series in Telecommunications and Signal Processing)
Keep in mind that the majority of the field is highly mathematical and there's no way of getting around it, so embrace the mathematics and delve right in! Many of the most advanced books get into analysis and measure theory, but generally with a reasonable amount of basic probability theory and a dash of combinatorics, you'll be fine.
A: A belated, but perhaps interesting addition.  Claude Shannon, did think and write about genetics.  The following link describes some of it: 
Shannon's Brief Foray into Genetics
A: "Information Theory, Inference, and Learning Algorithms" by David MacKay is very nice, & free pdf:
http://www.inference.phy.cam.ac.uk/mackay/itila/book.html
