"**A Mathematical Theory of Communication**" is an influential 1948 article by mathematician Claude E. Shannon. It was renamed **The Mathematical Theory of Communication** in the book, a small but significant title change after realizing the generality of this work.

The article was the founding work of the field of information theory. It was later published in 1949 as a book titled *The Mathematical Theory of Communication* (ISBN 0-252-72546-8), which was published as a paperback in 1963 (ISBN 0-252-72548-4). The book contains an additional article by Warren Weaver, providing an overview of the theory for a more general audience. Shannon's article laid out the basic elements of communication:

An information source that produces a message
A transmitter that operates on the message to create a signal which can be sent through a channel
A channel, which is the medium over which the signal, carrying the information that composes the message, is sent
A receiver, which transforms the signal back into the message intended for delivery
A destination, which can be a person or a machine, for whom or which the message is intended
It also developed the concepts of information entropy and redundancy, and introduced the term bit (which Shannon credited to John Tukey) as a unit of information.