While neural network control has been successfully applied in various practical applications, many important issues, such as stability, robustness, and performance, have not been extensively researched for neural adaptive systems. Motivated by the need for systematic neural control strategies for nonlinear systems, Stable Adaptive Neural Network Control offers an in-depth study of stable adaptive control designs using approximation-based techniques, and presents rigorous analysis for system stability and control performance. Both linearly parameterized and multi-layer neural networks (NN) are discussed and employed in the design of adaptive NN control systems for completeness. Stable adaptive NN control has been thoroughly investigated for several classes of nonlinear systems, including nonlinear systems in Brunovsky form, nonlinear systems in strict-feedback and pure-feedback forms, nonaffine nonlinear systems, and a class of MIMO nonlinear systems. In addition, the developed design methodologies are not only applied to typical example systems, but also to real application-oriented systems, such as the variable length pendulum system, the underactuated inverted pendulum system and nonaffine nonlinear chemical processes (CSTR).