The book provides a comprehensive introduction to NMPC and nonlinear adaptive control. In the first part of the book, a framework for the study, design, and analysis of NMPC systems is presented. The robustness of NMPC is presented in the context of this framework. The second part of the book presents an introduction to adaptive NMPC. Starting with a basic introduction to the problems associated with adaptive MPC, a robust set-based approach is developed. The third part of the book is dedicated to the practical realization of the adaptive NMPC methodology. An alternative approach to adaptive parameter estimation is first developed that yields a systematic set-based parameter estimation approach.The last part of the book presents a treatment of the discrete-time generalization of the continuous-time algorithms proposed in the third part of the book.