  This article serves as a brief introduction to the Shannon information
theory. Concepts of information, Shannon entropy and channel capacity are
mainly covered. All these concepts are developed in a totally combinatorial
flavor. Some issues usually not addressed in the literature are discussed here
as well. In particular, we show that it seems we can define channel capacity
differently which allows us to potentially transmit more messages in a fixed
sufficient long time duration. However, for a channel carrying a finite number
of letters, the channel capacity unfortunately remains the same as the Shannon
limit.
