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This text presents neural network theory for diverse applications in a unified way, where the structure of artificial neural networks are characterized by distinguished classes of graphs. The book first provides a clear but concise exposition of pseudoscience fundamentals, graph theory and algorithms. It then moves to a detailed analysis of perception and ls-theory based neural networks, multilayer feed forward networks, and self-organizing competitive learning neural networks. The text culminates with a chapter on selected applications. Developing graphing theory fundamentals for the systematic generation and characterization of ANN structures, students are not as confused by the multitudinous ANN structures that are present because they are using generic graphs to classify all structures. The use of MATLAB Toolbox to solve design problems heightens student awareness of powerful and convenient software that can be applied to design. By using growth and shrinkage networks for the modeling for biological neural network characteristics, students learn that to train only for interconnection weights is not sufficient - the structure must also be trained. The inclusion of applications, exceptions, myths and false claims is important, as supercomputing may not be successful in all applications, and the student needs to be aware of the potential and pitfalls of neuron as opposed to classical computing.