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With the development of science of intelligence, human being are exploring the mysteries of the brain. The brain is the most complex part of our body, and it is said that the brain is also the most complex organizational structure in the universe we have known. In order to reveal the farther nature of human intelligence, it is necessary to combine the biology and the information science, in order to promote the research of the human brain. Meanwhile, modern computer is far below the level of human brain in capacity of information processing in many aspects such as learning and cognizing, memory, thinking, reasoning, estimation. The scientists were inspirited by such contradiction to find a new way, naturally they went to the exploration of the human brain, so neural networks were born when the science of brain and the science of information met each other.The development of neural networks can not only facilitate the development of the science of intelligence greatly, so that to meet the demands of scientific research, but also stimulate the development of intelligent machines, so that to meet the demands of engineering. Therefore it is necessary to learn, to research and to innovate the neural networks.In this thesis, firstly I gave an overview of basic theory of the neural networks, after that I analysed the essence of the neural networks, when we understood the essence in mathematics of neural networks, I started from the principle of the feedforward neural networks combining with the feature of Taylor series, the feature of Fourier series, and the feature of Gauss function to make an innovation, to construct new neural networks based on Taylor series, in order to get a deep understanding of neural network theory and to provide applications in new ways. In order to show the theory, I didn’t care about the professional knowledge of the stock market in this thesis, just using the easy-to-understand stock price as the experimental data. I designed some experiments in the fields of forcasting for several common neural networks and the new innovation, in order to reveal and support the theory in different aspects. Finally, I gave a conclusion for this thesis and a prospect for advanced positions of the neural networks.
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