Network Coding Theory provides a tutorial on the basic of network coding theory. It presents the material in a transparent manner without unnecessarily presenting all the results in their full generality. Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory. The tutorial is divided into two parts. Part I is devoted to network coding for the transmission from a single source node to other nodes in the network. Part II deals with the problem under the more general circumstances when there are multiple source nodes each intending to transmit to a different set of destination nodes. Network Coding Theory presents a unified framework for understanding the basic notions and fundamental results in network coding. It will be of interest to students, researchers and practitioners working in networking research.