This book reports on the latest findings in the study of Stochastic Neural Networks (SNN). The book collects the novel model of the disturbance driven by Levy process, the research method of M-matrix, and the adaptive control method of the SNN in the context of stability and synchronization control. The book will be of interest to university researchers, graduate students in control science and engineering and neural networks who wish to learn the core principles, methods, algorithms and applications of SNN.