Network coding has been extensively studied for multicasting information in a directed communication network when communication links in the network are error-free. The network capacity for multicast satisfies the max-flow min-cut theorem, and this capacity can be achieved by network coding. In this thesis, we study the basic concepts of network error correction (NEC) as well as a framework for characterizing error correction and error detection capabilities of NEC codes. Moreover, different minimum distances are defined to measure error correction/detection capabilities. The error correction/detection capabilities of a network code is completely characterized by a parameter which is equivalent to the minimum Hamming distance when the network code is linear, and the weight measure on the error vectors is the Hamming weight. We study a deterministic and centralized algorithm which constructs a NEC code that attains the Singleton bound of network error correcting codes. Keywords: acyclic network, network coding, error correcting codes, linear network code, Singleton bound.