This book presents a novel inverse optimal control approach for stabilization and trajectory tracking of discrete-time nonlinear systems, avoiding the need to solve the associated Hamilton-Jacobi-Bellman equation, and minimizing a cost functional, resulting in efficient controllers. Additionally, the book proposes the use of recurrent neural networks as a tool to model discrete-time nonlinear systems; such models combined with the inverse optimal control constitute a powerful tool to deal with uncertainties such as unmodeled dynamics and disturbances. Different simulations illustrate the effectiveness of the synthesized controllers for stabilization and trajectory tracking of discrete-time nonlinear systems.