Abstract: In this paper, a mathematical theory of neural network learning is presented. According to this theory, different kinds of neural network learning can be treated in a unified way. The learning process of a neural network is considered the process in which neural network variables are changed with a time series of input signals generated from a stochastic information source.The self-adaption and self-organization of a neural system are the modification of neural network parameters so that it adapts to the environmental information structure.