Using real-life examples to illustrate the performance of learning algorithms and instructing readers how to apply them to practical applications, this work offers a comprehensive treatment of subspace learning algorithms for neural networks. The authors summarize a decade of high quality research offering a host of practical applications. They demonstrate ways to extend the use of algorithms to fields such as encryption communication, data mining, computer vision, and signal and image processing to name just a few. The brilliance of the work lies with how it coherently builds a theoretical understanding of the convergence behavior of subspace learning algorithms through a summary of chaotic behaviors.