In this book, several schemes for adaptive identification and observation of uncertain nonlinear systems are presented. Artificial neural networks, the Lyapunov stability theory and weight adjustment laws were used. Initially, an adaptive neural identification scheme wherein the estimation performance is directly related to two project matrices is studied, so it is simply necessary to adjust these matrices in order to obtain a residual state estimation error arbitrarily small. Then, it is considered a scheme characterized by being minimally influenced by disturbances, which is secured using a dynamic feedback gain in the identification model, defined by an adaptive law obtained based on the stability analysis. Finally, the study of a scheme for adaptive neural observation. Using the direct method of Lyapunov, it is shown that the observation residual state error depends directly from a scaling matrix defined by the user, which facilitates the application because it reduces the need to solve linear matrix inequalities to adjust the observation performance. In all presented schemes there was done an exhaustive simulation in order to prove the effectiveness of the theoretical schemes.